CARACAS, Venezuela — Secretary of State John Kerry said Wednesday that Venezuela should hold a recount of votes cast in its presidential election, which the country’s electoral authorities say was narrowly won by a protégé of former President Hugo Chávez.

The protégé, Nicolás Maduro, was declared the winner of Sunday’s special election with a margin of less than two percentage points over the opposition candidate, Henrique Capriles Radonski.

Mr. Capriles has refused to recognize the result, but has shown no hard evidence to back up his insistence that he won. He has also said there were numerous irregularities in the voting. On Wednesday, he formally submitted his request for a recount.

Mr. Kerry, in comments to a House committee, said, “We think there ought to be a recount.” He added that he had not yet evaluated whether Washington would recognize Mr. Maduro’s victory.

In a televised meeting with governors on Wednesday, Mr. Maduro responded, saying: “Take your eyes off of Venezuela, John Kerry. Get out of here. Enough interventionism.”

Also on Wednesday, the president of the Supreme Court, Luisa Morales, rejected the idea of a recount, saying it was impossible.