Venezuela teetered on the brink of a political crisis Monday after President Nicolas Maduro claimed reelection amid contested and seemingly suspicious vote tallies, while the Biden administration cast heavy doubt on the results and critics said Mr. Maduro’s socialist government had flagrantly overturned the will of the country’s voters.

Edmundo Gonzalez Urrutia, a retired diplomat and Mr. Maduro’s opponent, suggested that the official government vote totals were fraudulent and he was the rightful winner.

The election stakes were high. U.S. adversaries such as Russia and China are cultivating closer ties with oil-rich Venezuela to help them strengthen their foothold in South America.

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The Biden administration immediately demanded that Venezuela release precinct-level vote totals, citing preelection and exit polls showing the opposition with a significant lead.

“By engaging in repression and electoral manipulation, and by declaring a winner without the detailed precinct-by-precinct polling results … to support a claim, Maduro representatives have stripped the supposed election results they announced of any credibility,” a senior U.S. administration official told reporters in a background briefing.

Caracas was said to be tense but peaceful throughout much of the day Monday as both sides rushed to shore up their claims to electoral victory. But by Monday evening, thousands of protesters were in the streets demonstrating against the official government results.

Some were reportedly headed toward the presidential palace in Caracas. 

Earlier in the day, Moscow and Beijing congratulated Mr. Maduro on his “victory” shortly after Venezuela’s National Electoral Council, which is loyal to Mr. Maduro’s ruling socialist party, announced the results.

Leaders across Latin America said the election must be fully reviewed.

According to the official government totals, 51% of the vote Sunday went to Mr. Maduro and 44% to Mr. Gonzalez. Those figures differ wildly from independent exit polling conducted by Edison Research, which sampled nearly 7,000 voters at 100 polling sites across Venezuela.

About 65% of voters backed Mr. Gonzalez, compared with just 31% for Mr. Maduro, according to those Edison exit surveys.

Mr. Gonzalez and his allies told reporters late Monday that they had obtained more than 70% of government vote tally sheets, and those documents mirrored the exit polls, showing Mr. Gonzalez with more than twice as many votes as Mr. Maduro. Those figures had not been independently verified as of Monday evening.

Mr. Maduro, a protege of the late anti-U.S. populist Hugo Chavez seeking a third six-year term, sought to stop a brewing political crisis before it had the chance to start. He appeared Monday at a nationally televised ceremony and unequivocally declared victory.

“We have never been moved by hatred. On the contrary, we have always been victims of the powerful,” he said. “An attempt is being made to impose a coup d’etat in Venezuela again of a fascist and counterrevolutionary nature.

“We already know this movie, and this time, there will be no kind of weakness,” Mr. Maduro said.

Before Mr. Maduro’s public comments, Mr. Gonzalez made clear that he did not believe the official figures from Caracas, where Mr. Maduro’s United Socialist Party of Venezuela controls all three branches of government.

“Venezuelans and the entire world know what happened,” said Mr. Gonzalez, urging his supporters to remain calm.

It wasn’t immediately clear what Mr. Gonzalez intended to do next. Legal challenges are a certainty, though the tight grip of Mr. Maduro’s party over the Venezuelan political system means such challenges may accomplish little.

As protests erupted Monday night, Mr. Gonzalez called on supporters to gather Tuesday morning to celebrate the results of the election, the Associated Press reported.

Mr. Maduro’s socialist party has controlled Caracas for 25 years, beginning with Chavez’s ascent to power in 1999. Under pressure to ease harsh U.S. and international sanctions on his economy, Mr. Maduro sought reelection to his third six-year term amid deep turmoil.

Venezuela sits atop the world’s largest oil reserves and once boasted Latin America’s most advanced economy. After Mr. Maduro came to power, the economy tumbled into a free fall marked by plummeting oil prices, widespread shortages of basic goods and hyperinflation of 130,000%.

Taking sides

Global powers split over whether to accept the official election results from Caracas. Speaking to reporters in Tokyo, Secretary of State Antony Blinken cast doubt on the Venezuelan government’s tallies.

“We have serious concerns that the result announced does not reflect the will or the votes of the Venezuelan people,” Mr. Blinken said. “It’s critical that every vote be counted fairly and transparently, that election officials immediately share information with the opposition and independent observers without delay, and that the electoral authorities publish the detailed tabulation of votes. The international community is watching this very closely and will respond accordingly.”

Josep Borrell, the European Union’s top diplomat, expressed similar sentiments.

“The people of Venezuela voted on the future of their country peacefully. … Your will must be respected,” he said in a post on X, according to English-language translations. “It is vital to ensure full transparency of the electoral process, including detailed vote counting and access to polling station voting records.”

At least eight Latin American nations called for an emergency meeting of the Organization of American States.

“We are putting diplomatic relations on hold until a complete review of the voting records and of the voting computer system is carried out,” Panamanian President Jose Raul Mulino said at a news conference, according to Reuters.

China and Russia took the opposite tack, as did friendly left-leaning Western Hemisphere regimes in Cuba and Bolivia.

“China congratulates Venezuela on the smooth presidential election and congratulates President Nicolas Maduro on his successful reelection. China and Venezuela are good friends and partners that support each other,” Chinese Foreign Ministry spokesperson Lin Jian told reporters at a press conference in Beijing.

In Moscow, Russian President Vladimir Putin congratulated Mr. Maduro and said he hopes their two nations can “continue our constructive joint work on key issues on the bilateral and international agenda.”

For Russia and China, Venezuela is an important military, economic and diplomatic ally in the Western Hemisphere.

Venezuela provides China with a significant amount of oil, among other ties. Russia views Venezuela as a strategically vital military partner. Earlier this month, two Russian warships docked at the Venezuelan port of La Guaira after exercises in the Atlantic Ocean.

The Biden administration earlier this year offered to ease economic sanctions if Mr. Maduro agreed to allow free and fair elections. The offer sparked criticism on Capitol Hill.

“I am concerned but not surprised that Nicolas Maduro is tightening his grip on Venezuela,” Sen. James E. Risch of Idaho, the ranking Republican on the Senate Foreign Relations Committee, said in a statement Monday. “To be sure, Maduro is reaping the benefits of three years of appeasement policies by the Biden-Harris administration.”

The senior U.S. official would not detail the Biden administration’s next steps as the election results are being tabulated but said Washington was prepared to rally allies in the region and globally against any attempt to steal the election.

“I don’t think we’re going to get into the details of how we would respond, but I will note that numerous nations and institutions in the international community have already expressed concerns about the current situation,” the official said.

• This article is based in part on wire service reports.