Both Trump's and Peña Nieto's offices released readouts of the call, saying the two leaders spoke about the importance of their relationship and issues -- such as stemming the sale of illegal drugs and arms -- that they could work on together. But the respective statements differed on one key point: a promise, per the Mexican side, to not speak publicly about who would pay for the wall.
"With regard to the payment of the border wall, both Presidents acknowledged their clear and very public differences in position on this sensitive issue," the Mexican statement said. "The Presidents also agreed at this point not to speak publicly about this controversial issue."
The White House statement included near identical language on the border wall, but didn't mention a pledge not to speak publicly about the issue.
White House Press Secretary Sean Spicer told reporters later Trump did agree to not publicly talk about how the border wall will be funded during the call with Peña Nieto.
"They agreed not to discuss how it will be paid for publicly, that they will continue to have those discussion privately," Spicer said.
When asked why that information was not in the White House statement, Spicer said: "Ask the (Mexican) President why he wanted to put it out."
During a news conference at the White House on Friday, Trump did not mention building the wall.
The Trump-Peña Nieto discussion comes after the Mexican president canceled a meeting with Trump that had been set for next week after the White House moved forward with plans to build a wall along the US-Mexico border and Trump tweeted that the meeting shouldn't go ahead if Mexico wasn't prepared to pay for its construction.
At White House news conference with British Prime Minister Theresa May, Trump was asked about the call and described a "very, very friendly" conversation with Peña Nieto, at the same time insisting he would maintain a tough stance on trade with the US neighbor.
"Mexico ... has out-negotiated us and beat us to a pulp through our past leaders," Trump said. "They have made us look foolish."
The President said he would work to bolster a "soft and weak" border and prevent American jobs from moving across the border.
"We're no longer going to be the country that doesn't know what it's doing," Trump said.
Thursday was a low point in the relationship between the two leaders.
"This morning we have informed the White House that I will not attend the meeting scheduled for next Tuesday with the POTUS," Peña Nieto tweeted Thursday.
"If Mexico is unwilling to pay for the badly needed wall, then it would be better to cancel the upcoming meeting," Trump tweeted before the meeting was canceled.
White House press secretary Sean Spicer endorsed the idea of a 20% border tax on goods from Mexico on Thursday as a way to fund the wall, estimated to cost $12-$15 billion. But he later said that was only one of many options under consideration. It is controversial among Republicans on Capitol Hill, with critics saying the tax would be passed on to consumers in the United States.