CNBC/AP

Mexican President Enrique Peña Nieto and President Donald Trump have come up with a temporary solution to their dispute over Trump's proposed border wall: keep the public out of it.

During an hour-long call on Friday morning, the two sides "agreed at this point not to speak publicly" about the American leader's plan to build a border wall and make the people of Mexico pay for its construction, the Mexican government said in a press release.

That news comes after Peña Nieto cancelled a scheduled meeting this week with Trump after the former reality TV star tweeted they should call the meeting off "if Mexico is unwilling to pay for the badly needed wall." Trump has signed an executive order to immediately begin constructing the massive wall, part of the new president's sweeping immigration crackdown.

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In a joint press conference with UK Prime Minister Theresa May Friday afternoon, Trump confirmed he had a "very, very friendly" call with Peña Nieto on Friday morning.

"We’re going to be working on a fair relationship and a good relationship," Trump said of relations with Mexico.

A statement from the White House about the meeting did not mention an agreement to stop talking publicly about the wall but acknowledged the leaders' "clear and very public differences of positions on this issue."