MEXICO CITY — The United States appears to have thrown its weight behind President Juan Orlando Hernández of Honduras, who was declared the winner of last month’s disputed election, ignoring a call from the Organization of American States for a repeat of the voting.

Both Mr. Hernández and his opponent, Salvador Nasralla, held fast to their positions on Tuesday. The president, who is seeking a second term, took on the tone of a generous winner in a televised address in which he offered his “undying gratitude” to those who had voted for him and called for “national understanding.”

Mr. Nasralla amplified the O.A.S. recommendations for a new election during a two-day trip to Washington. Speaking to reporters, he urged other countries not to recognize Mr. Hernández as the winner of the election and to suspend aid to the Honduran government until a new vote is negotiated.

“In the exercise of democracy, a candidate cannot ignore the O.A.S.,” he said.

Although Washington has yet to recognize Mr. Hernández as the winner of the election, the State Department said in a statement on Monday that “the United States notes that Honduras’ Supreme Electoral Tribunal has declared incumbent president Juan Orlando Hernández the winner” of the election. In its statement, the State Department called on the opposition to file its complaints with the electoral authorities.