Hondurans seek a break from graft and despair in an election with repercussions for the United States.

TEGUCIGALPA, Honduras — Hondurans voted Sunday in tense general elections that are likely to have repercussions far beyond the Central American country.

For the opposition, the elections represent a chance to reinstate the rule of law after eight years of systematic dismantling of democratic institutions by the departing president, Juan Orlando Hernández.

The stakes are arguably even higher for the leaders of the party in power. If they lose the protections afforded by being in office, they could face charges of corruption and drug trafficking in investigations conducted by prosecutors in the United States and Honduras.

Both main political parties claimed to have won in nearly identical Twitter messages posted while people were still casting votes in the late afternoon.

The elections are being closely watched in Washington.

Having made Central America a foreign policy priority, the Biden administration has not stemmed the tide of authoritarianism and corruption in the region. The country’s economic and political malaise, as well as chronic violence, is driving Hondurans to join the tens of thousands of Central Americans heading to the United States’ southern border every month, leading to Republican attacks and potentially damaging Democratic prospects in the upcoming midterm elections.

Polls show a tight race between the candidate of the governing National Party, Nasry Asfura, the charismatic mayor of the capital, Tegucigalpa; and Xiomara Castro, the wife of Manuel Zelaya, a leftist former president deposed in a 2009 coup. Both candidates, in different ways, promise a break with Mr. Hernández’s deeply unpopular government.

Both sides have portrayed the elections as the decisive battle for the country’s destiny. But the prospects for radical change are poor: The main parties in Honduras have all been marred by accusations of corruption or links with organized crime.

“At best, you will get an outcome that won’t be great,” said Daniel Restrepo, a fellow at the Center for American Progress, a Washington, D.C., think tank, who was a senior adviser on Latin America to President Barack Obama. “The hope is to inject more legitimacy into the system.”

A more responsive government with a strong popular mandate, he said, could also help stem migration.

“If people think their voices are not being heard, they are more likely to leave,” he said.

A legitimately elected new president could provide the Biden administration with a desperately needed partner in a region whose leaders are increasingly challenging Washington’s economic and political influence.

The governments of all three nations bordering Honduras have further dismantled U.S.-backed democratic checks on their power since President Biden took office, despite his administration’s promise to spend $4 billion to fight corruption and impunity as two of the root causes of migration.

Nicaragua’s authoritarian president, Daniel Ortega, jailed every credible opposition candidate who might have challenged him, allowing him to win a fourth consecutive term practically unopposed in an election this month.

In Guatemala, the government disbanded an anti-corruption investigative body and arrested some of its prosecutors after they began looking into allegations of bribery involving President Alejandro Giammattei.

And the president of El Salvador, Nayib Bukele, is quashing independent voices and openly challenging the United States as he accumulates power, prompting Washington’s top diplomat to leave the country this month for lack of cooperation from the Salvadoran government.

In Honduras itself, American and Honduran prosecutors accuse Mr. Hernández of building a pervasive system of graft, allowing drug trafficking organizations to penetrate every level of his government. His brother, Tony Hernández, is serving a life sentence in the United States for helping ship tons of cocaine, in a case that has also named the president a co-conspirator.

The president, Mr. Hernández, has denied all accusations against him and has not been charged with any crime.