Trump meets Mexican President
Trump on Wednesday said they did not discuss his plan to make Mexico pay for the wall - a central plank of his campaign.
"We did discuss the wall. We didn't discuss payment of the wall. That'll be for a later date. This was a very preliminary meeting," EFE news quoted the magnate as saying during a joint press conference with Pena Nieto at the Mexican presidential mansion.
But Pena Nieto later tweeted: "I made it clear Mexico would not pay for the wall".
The two men spoke after meeting privately.
"Cooperation toward achieving the shared objective - and it will be shared - of safety for all citizens is paramount, to both the US and to Mexico," the magnate said.
The US presidential hopeful began by thanking Pena Nieto for the invitation and said that he and his host were "united by our support for democracy, a great love for our people and the contributions of millions of Mexican-Americans to the US."
While offering no apology for his previous characterization of Mexican immigrants to the US as "criminals" and "rapists," Trump spoke of his "great respect" for Mexican-Americans and "their strong values of family, faith and community".
Ending illegal immigration was the first item on a list of "shared goals" Trump proposed for the US and Mexico.
"This is a humanitarian disaster. The dangerous treks, the abuse by gangs and cartels and the extreme physical dangers, and it must be solved, it must be solved quickly," the Republican candidate said.
The statements from Pena Nieto and Trump were followed by a brief question-and-answer session with reporters.
Pena Nieto invited both Trump and Democratic candidate Hillary Clinton to Mexico.
The Mexican president said during the press conference that he extended the invitations in the interest of promoting bilateral cooperation, expressing "absolute respect for the election process in the US".
However, Pena Nieto has faced heavy criticism over inviting Trump to Mexico and holding talks.
Former President Vicente Fox told CNN: "We don't like him. We don't want him. We reject his visit."
Former First Lady Margarita Zavala tweeted: "We Mexicans have dignity, and we reject your hate speech."
At least two demonstrations have been planned in Mexico City.