"We understand and respect her decision to propose the time to hold a meeting," said Mexican Foreign Minister Claudia Ruiz Massieu in a tweet, adding that contact with Clinton's campaign was ongoing.
Pena Nieto extended invitations to both candidates last month, and Trump flew to Mexico City last Wednesday for a meeting that appeared to be friendly but later revealed deep tensions.
Trump, the Republican presidential nominee, has been highly critical of Mexico, saying the country sends rapists and drug dealers to the United States. He has called for a wall to be built on the border that would be paid for by Mexico.
Trump said at a joint news conference with Pena Nieto that they did not discuss who would pay for the wall. Pena Nieto remained silent on the issue at the event, but said later on Twitter that he made it clear Mexico would not pay for the wall.
"He came out saying one thing and the Mexican president contradicted him almost immediately," Clinton, a former U.S. secretary of state, said in the ABC interview.
"He didn't raise it, so he did choke. He didn't know how to even communicate effectively with a head of state. And I think that's a pretty clear outcome from that trip," she added.