President Juan Orlando Hernández, a conservative hoping to win a second term, has been a willing partner on the concerns that matter most to the United States. And as he increased control over every branch of the government since his election in 2013, no objections were raised from the Obama or Trump administrations — not even when his handpicked Supreme Court justices found a circuitous way to lift the prohibition on running for re-election.

How well the White House navigates a resolution of the contested election may not only affect Honduran democracy but also could resound across the region, where elections are scheduled over the next year in seven countries, including Brazil, Mexico, Venezuela and Colombia.

“Will the United States remain consistent in defending the electoral process, regardless of whether the country in question is friend or foe,” wrote Juan Gonzalez, an adviser to former Vice President Joseph R. Biden Jr. on Central America, in an email, “or equivocate when the process breaks down in a country that cooperates with the United States?”

More than two weeks after Hondurans voted, the election outcome is still in doubt. According to the count by the electoral commission, which is controlled by Mr. Hernández’s allies, the president won nearly 52,500 more votes than his main opponent, Salvador Nasralla, who leads a leftist coalition.