US President Donald Trump urged his Mexican counterpart, Enrique Peña Nieto, to stop saying that his country will not pay for the controversial border wall at the same time that he admits the difficulties in forcing that country to do so, The Washington Post reported Thursday.

"You cannot say that to the press," Trump said in a Jan. 27 telephone call to the Mexican leader, the transcript of which the Post obtained.

"If you are going to say that Mexico is not going to pay for the wall, then I do not want to meet with you guys anymore because I cannot live with that," Trump reportedly said.

Instead of saying "We will not pay," Trump proposed that both leaders - when asked about paying for the wall - should simply say, "We will work it out."

"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," Trump told Peña Nieto. "I have been talking about it for a two-year period, and the reason I say they are going to pay for the wall is because Mexico has made a fortune out of the stupidity of US trade representatives."

The controversial proposal to build a border wall to reduce - if not halt - illegal immigration from Mexico to the US was one of Trump's key campaign and oft-repeated promises.

However, in his chat with the Mexican president, Trump said that, from an economic point of view, the wall was "the least important thing we were talking about, but psychologically, it means something."

Peña Nieto, meanwhile, reiterated that his "position has been and will continue to be very firm saying that Mexico cannot pay for that wall."

"This is an issue related to the dignity of Mexico and goes to the national pride of my country," he added.

During the conversation, Trump went so far as to threaten to impose additional tariffs of 35 percent on Mexican imports, given - he said - that the US president has extensive power regarding customs duties.

In the US, lawmakers acknowledge the difficulty of forcing Mexico to pay for the proposed border wall, and Trump himself has said that Washington will put up the money and only later seek a way in which Mexico would "reimburse" it for the cost.

Meanwhile, the House of Representatives approved some $1.6 billion requested by the White House to begin construction of several stretches of wall, although it will be very tough to get the Senate to follow suit.