Donald Trump downplayed the economic importance of his promised border wall to the Mexican president, according to a leaked transcript of their conversation.
The US president also pleaded with Enrique Pena Nieto not to state publicly that his country would not pay for a border wall.
The transcript of their conversation held on January 27 was leaked to the Washington Post on Thursday.
The proposed wall was a huge point for Mr Trump in the election campaign during which he repeatedly vowed that Mexico would pay for it.
But during the conversation, he said: "From an economic issue, it is the least important thing we were talking about, but psychologically, it means something so let us just say, 'We will work it out.'"
He conceded in the conversation held shortly after he took office that he is in a "political bind" over who will pay for its construction.
"My people stand up and say, 'Mexico will pay for the wall' and your people probably say something in a similar but slightly different language," he said.
"But the fact is we are both in a little bit of a political bind because I have to have Mexico pay for the wall – I have to.
"I am willing to say that we will work it out, but that means it will come out in the wash and that is okay."
The conversation, on the same day Prime Minister Theresa May visited Mr Trump at the White House, lays bare how keen Mr Trump is to be portrayed favourably by the press despite his regular tirades against the media.
Mr Nieto said: "But my position has been and will continue to be very firm saying that Mexico cannot pay for that wall."
Mr Trump replied: "But you cannot say that to the press. The press is going to go with that and I cannot live with that."
The Post also leaked his conversation the following day with Australian Prime Minister Malcolm Turnbull.
A White House statement on the phone call made it seem to be a more cordial affair but the transcript shows Mr Trump's anger over a refugee agreement with Australia.
"As far as I am concerned that is enough Malcom (sic). I have had it. I have been making these calls all day and this is the most unpleasant call all day. Putin was a pleasant call. This is ridiculous," Mr Trump said.