Donald Trump has insisted that Mexico will pay for the wall he wants to build along the length of the border with the US.
He said during a speech on immigration in Phoenix, Arizona that Mexico will pay for the wall "100 per cent" and added: "They don't know it yet, but they're going to pay for" it.
The Republican presidential candidate earlier met Mexico's president and said they had not discussed who would pay for the massive wall that has been at the centre of his White House campaign.
But President Enrique Pena Nieto tweeted: "At the beginning of the conversation with Donald Trump, I made clear that Mexico would not pay for the wall."
The two men met privately in Mexico City on Wednesday afternoon.
Mr Pena Nieto is undergoing a public relations disaster after his decision to meet Mr Trump, perhaps Mexico's most-disliked man.
The decision is being called a national humiliation by social media posters and politicians who say it is likely to reduce the president's already low popularity ratings.
Mr Pena Nieto did not demand that the US Republican presidential candidate apologise for calling Mexican migrants rapists and criminals.
He also stood by silently at their joint press conference as Mr Trump repeated his pledge to build a border wall between the two countries.
Many Mexicans wonder why Mr Pena Nieto agreed to the encounter.
"This is an insult and a betrayal," artist Arturo Meade said as he joined a protest against Wednesday's meeting in Mexico City.
Televisa news anchor Carlos Loret de Mola tweeted "The humiliation is now complete" as he marvelled that Mr Trump would dare come to Mexico and reiterate his intention to build the wall.
Mexicans were particularly annoyed that Mr Pena Nieto appeared to do little to push back against Mr Trump's earlier negative statements about Mexican migrants and unpopular proposals.
Mr Pena Nieto "did not even take a really strong stand and talk to Mr Trump directly to his face and tell him exactly why his stances are not acceptable to Mexicans," Tony Payan, director of the Mexico Centre at Rice University's Baker Institute, said.
"He sounded tepid and too soft. He essentially rolled over and allowed Mr Trump to get away with his own goals without getting anything in return."
Dr Payan thought the president had little good news to give in his state-of-the-nation address scheduled for Thursday and was looking for a distraction with the "ill-advised" meeting.
"Maybe Pena saw the opportunity to distract the attention of the Mexican people," he said.
Mr Pena Nieto did say Mexicans felt aggrieved and had disagreements with Mr Trump but most felt that this was not enough.
Mr Trump gained a little with the meeting but Mexico's president lost a lot, Javier Urbano Reyes, a professor in the department of International Studies at the Iberoamerican University in Mexico City, said.
"Without a doubt, my perception is that it is going to make it even worse, even stronger the drop in approval," he said of Mr Pena Nieto's near 20 per cent approval rating.
Former Mexican president Vicente Fox said Mr Trump was trying to boost his sagging campaign, adding: "He fooled [Mr Pena Nieto]."
Writer Angeles Mastretta tweeted that Mexicans saw "what was expected: a president who isn't capable of demanding apologies ... how sad."
Mr Pena Nieto and Mr Trump even appeared to disagree about what was said in the meeting.
Mr Trump said the topic of who would pay for the wall would be discussed later, as he stood next to Mr Pena Nieto who said nothing about the wall.
The president said in a tweet hours later that he had told Mr Trump clearly in their private meeting that Mexico would not pay.
It seemed to contradict Mr Trump's statement that payment was not discussed, but the president's office said only that Mr Pena Nieto made his statement and the topic was dropped.
Mr Trump later made building the wall the featured element of his immigration plan in a speech on immigration in Phoenix, Arizona.
He referred to Mr Pena Nieto as a "wonderful, wonderful president" but reaffirmed the pledge he had not repeated in Mexico: "They don't know it yet, but they're going to pay for the wall."
