The conversation was reported hours after Trump took to Twitter again to rail against Mexico.
"Mexico has taken advantage of the US for long enough," Trump said Friday, writing first on his personal Twitter account and then re-tweeting the message under his presidential handle.
"Massive trade deficits & little help on the very weak border must change, NOW!" he added.
Trump has angered Mexicans, perplexed economists and energized his nationalist political base by vowing to build a wall along the US frontier - and then somehow to make Mexico pay for it.
His insistence on this point caused Pena Nieto - who had voiced optimism that he could have good relations with Trump after the US election - to cancel a planned visit to Washington next week.
Putin, Trump to speak by phone for first time on Saturday
Economy Minister Ildefonso Guajardo, who met with US officials in Washington this week, told the Televisa network that the two sides were "at an impasse."
But the line of communication remains open, maintaining "the possibility to find a solution," he said.
Analysts say the spat has created the biggest diplomat rift since a drug cartel tortured and killed a US undercover agent in 1985.
Mexico's leaders have repeatedly said their country will never pay for the 2,000-mile (3,200-kilometer) border barrier that Trump says is needed to stop illegal immigrants and drug smugglers coming over.
Trump's response has been to ask the US Congress to find between $12 and $15 billion for construction and to help him find a way to recoup the money with some kind of tariff on Mexican imports.
His team have floated several ideas for how to do this. On Friday, for example, senior aide Kellyanne Conway told CBS television that a five to 20 percent tax may be imposed at the border.
On Thursday, White House spokesperson Sean Spicer suggested that one option - not necessarily the favored one - would be a border adjustment tax of the kind favored by Republicans in the US Congress.
Visiting Washington on Thursday, Mexico's Foreign Minister Luis Videgaray scoffed at the notion, arguing that this would just pass the cost of the wall on to US consumers of Mexican goods.
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