The Biden administration and European allies call President Vladimir V. Putin of Russia a tyrant and a war criminal. But he enjoys a standing invitation to the halls of power in Brazil.

The president of Brazil says that Ukraine and Russia are both to blame for the war that began with the Russian military’s invasion. And his nation’s purchases of Russian energy and fertilizer have soared, pumping billions of dollars into the Russian economy.

The views of the president, Luiz Inácio Lula da Silva, encapsulate the global bind in which the United States and Ukraine find themselves as the war enters its third year.

When Russia launched its full-scale invasion of Ukraine on Feb. 24, 2022, the Biden administration activated a diplomatic offensive that was as important as its scramble to ship weapons to the Ukrainian military. Wielding economic sanctions and calling for a collective defense of international order, the United States sought to punish Russia with economic pain and political exile. The goal was to see companies and countries cut ties with Moscow.

But two years later, Mr. Putin is not nearly as isolated as U.S. officials had hoped. Russia’s inherent strength, rooted in its vast supplies of oil and natural gas, has powered a financial and political resilience that threatens to outlast Western opposition. In parts of Asia, Africa and South America, his influence is as strong as ever or even growing. And his grip on power at home appears as strong as ever.

The war has undoubtedly taken a toll on Russia: It has wrecked the country’s standing with much of Europe. The International Criminal Court has issued a warrant for Mr. Putin’s arrest. The United Nations has repeatedly condemned the invasion.

And to hear Biden administration officials tell it, Russia has suffered a major strategic failure.

“Today, Russia is more isolated on the world stage than ever,” Secretary of State Antony J. Blinken declared in June. Mr. Putin’s war, he added, “has diminished Russian influence on every continent.”

Beyond North America and Europe, there is evidence to the contrary.

China, India and Brazil are buying Russian oil in record quantities, feasting on the steep discounts Mr. Putin now offers to countries willing to replace his lost European customers. With those growing economic relationships have come strong diplomatic ties, including with some close U.S. partners. Mr. Putin visited Beijing in October and hosted India’s foreign minister in Moscow in late December. A few weeks earlier, Mr. Putin was warmly received in Saudi Arabia and the United Arab Emirates, where he was greeted with a 21-gun salute and fighter jets overhead trailing smoke in the red, white and blue of Russia’s flag.

Russian influence is also expanding in Africa, according to a new report from the Royal United Services Institute, a security research group based in London. When Yevgeny V. Prigozhin, the leader of the Wagner mercenary group, died last summer, Russia’s military intelligence service took over Wagner’s extensive operations in Africa and made further inroads with governments that rely on the group for security.

“By no means is Russia boxed in,” said Michael Kimmage, a Cold War historian at the Catholic University of America who was a State Department official in the Obama administration. “It’s not boxed in economically, it’s not boxed in diplomatically and it gets its message out on the war.”

To some Russia experts, American and European leaders have not fully reckoned with this reality.

“What Western leaders conspicuously haven’t done is level with their publics about the enduring nature of the threat from an emboldened, revisionist Russia,” Eugene Rumer and Andrew S. Weiss of the Carnegie Endowment for International Peace wrote in November in an essay for The Wall Street Journal accusing the West of “magical thinking” about Mr. Putin’s plight.

A prime example of the disappointment is Mr. Putin’s welcome mat in Brazil, Latin America’s largest and most globally influential nation.

Mr. Lula has extended an invitation to Mr. Putin to attend a Group of 20 leadership summit in Brazil in November, even though his country is a member of the International Criminal Court and is obliged to enforce the court’s arrest warrant for the Russian leader. (Mr. Lula sidestepped questions in December about whether Mr. Putin would be arrested if he showed up, calling it a “judicial decision.”)

Brazil’s persistently neutral stance on Russia’s war in Ukraine came up in a meeting on Wednesday in Brasília, the nation’s capital, between Mr. Lula and Mr. Blinken. Mr. Lula has called for peace talks, a position that Ukraine has criticized, and has said the United States is fueling the war with its weapons shipments to Kyiv. Mr. Blinken told Mr. Lula that the United States did not think conditions were right for diplomacy now.

Later that day, Mr. Blinken landed in Rio de Janeiro for a meeting of foreign ministers from the Group of 20 nations and heard Brazil’s top diplomat, Mauro Vieira, say, “Brazil does not accept a world in which differences are resolved by using military force.”

Sergey V. Lavrov, Russia’s foreign minister, was present. While Mr. Blinken and a handful of counterparts from allied nations denounced Russia’s war, the other officials followed the Brazilian minister’s lead in voicing neutral sentiments or stayed silent on the conflict.

At a news conference on Thursday, Mr. Blinken asserted that Mr. Lavrov had heard criticism throughout the meeting, saying there was a “very strong chorus” that spoke on “the imperative of ending the Russian aggression.”

Last year, Mr. Lavrov attended a similar event in India. He visited more than a dozen African nations in 2023, including South Africa, Sudan and Kenya. And he was welcomed last April by Mr. Lula at the presidential residence, and was expected to see the Brazilian president again in Brasília on Thursday.

He met in New York last month with António Guterres, the secretary general of the United Nations — which Russia’s foreign ministry advertised in a news release that showed the two men shaking hands.

At the United Nations, U.S.-led resolutions condemning the war have found little support among countries that are not closely aligned with the United States or Russia, demonstrating their reluctance to be forced to take a side in the conflict.

“These countries are wary of being seen as pawns on a chessboard of great-power competition,” said Alina Polyakova, the president of the Center for European Policy Analysis in Washington. “The last administration did a lot of damage to our relationship with a lot of these countries. We haven’t been seen as a credible partner.”

“Russian disinformation has been effective in a lot of places,” she added. “And in a lot of these countries, Russia has invested for decades.”

Moscow has also worked to avoid blame for higher food and energy prices that followed its invasion. Several weeks ago, Russia delivered 34,000 tons of free fertilizer to Nigeria, one of several such shipments it has sent to Africa.

Mr. Putin can afford such largess, not to mention a war of attrition in eastern Ukraine, because Russia has replaced lost energy customers in Europe by selling far more on other continents. The International Energy Agency reported last month that Russia exported 7.8 million barrels of oil per day in December, the highest in nine months — and only slightly below prewar levels.

At the same time, its oil export revenues were $14.4 billion that month, the lowest in a half-year. The agency said Western efforts to enforce a price cap on Russian oil appears to have bitten into overall revenues, as has a decrease in the global market price of crude oil.

Russia’s standing is benefiting from President Biden’s support for Israel’s war in Gaza, analysts say. Many leaders see hypocrisy in American condemnations of Russian strikes on civilian areas and infrastructure in Ukraine, unmoved by the argument that Israel works to avoid civilian casualties while Russia has deliberately targeted innocents.

Beyond that, Russia has succeeded in forming tighter bonds with its close partners, what Ms. Polyakova calls a “new authoritarian alliance.” Those countries — China, North Korea and Iran — have given aid to Moscow in various forms. North Korea is sending ballistic missiles for use in Ukraine, Iran continues to ship drones and China, while refraining from exporting arms to Russia, is allowing equipment that civilians and the military can use to get into Moscow’s hands.

China has kept up commerce with Russia and is filling in gaps left by Western companies, ensuring a supply of everything from household goods to financial services.

As for sanctions meant to limit Russia’s access to high technology, particularly equipment that could be used for modern weapons, Mr. Putin has found workarounds. Nearby countries like Armenia and Turkey, a member of the North Atlantic Treaty Organization, have not joined the U.S. sanctions regime, and private companies there import microchips and other items for re-export to Russia.

Western sanctions and business boycotts have certainly affected daily life in Russia, though in many cases through inconveniences like the loss of Apple Pay and Instagram — not enough to foment popular unrest or change Mr. Putin’s behavior.

“In the here and now, the sanctions have disappointed,” said Edward Fishman, a former State Department official in the Obama administration who oversaw Russia sanctions after Mr. Putin annexed Crimea in 2014.

Over time, Mr. Fishman said, Western sanctions will take a greater toll. Despite loopholes and black market trade, Russia will struggle to acquire critical high-technology components. And ruptured deals with Western energy companies will deprive Russia of the investment it needs to maintain efficient oil and gas production.

But he said that Mr. Putin had prepared his country for an onslaught of sanctions, and that he had come up with enough options to maintain his war machine and leverage on the world stage.

“Unfortunately, Russia has now built a kind of alternative supply chain,” said Mr. Fishman, a senior research scholar at Columbia University.

He added that Mr. Biden could take even bolder steps to crack down on Russian energy exports and technology imports. But that would mean friction with nations that have become major buyers of Russian oil, like India, who might reduce their imports only under the threat of sanctions or other punitive measures that could risk a diplomatic crisis.

Similarly, many businesses enjoying big profits from serving as middlemen for banned technology items are in Turkey and the United Arab Emirates, two partners whom Mr. Biden would rather not confront.

Perhaps most daunting is the fact that curtailing Russian oil exports is likely to drive up global oil prices — bad news for the United States and a president facing voters this fall.

“I think there’s a lot of nerves about doing anything that can rattle global oil markets,” Mr. Fishman said, “especially in an election year.”