Donald Trump kicked off a long-awaited speech in Arizona on immigration saying his plan will not offer a path to legal status or citizenship.
He vowed anyone who is in the United States illegally will face deportation if he's elected, and would-be immigrants would have to re-apply for re-entry.
The speech came hours after a meeting with Mexico's president, Enrique Pena Nieto.
Mr Trump spoke of Mexican-Americans in glowing terms and stressed the areas of common interest, such as stopping the flow of illegal drugs across the border, and a shared goal to put drug cartels out of business.
At the same time he stuck to his message that he would put up a wall.
When he got to Arizona, Mr Trump repeated his promise and insisted that Mexico would pay for it.
"Mexico will pay for the wall. 100 per cent. They don't know it yet but they're gonna pay for the wall. And they're great people and great leaders but they're gonna pay for the wall. On day one, we will begin working on an impenetrable, physical, tall, powerful, beautiful southern border wall."
Hours after Mr Trump's comments, Mr Nieto tweeted his version of the meeting, saying at the beginning of the conversation with MrTrump, he made it clear that Mexico would not pay for the wall.
At the launch of his presidential bid in June last year, Mr Trump accused Mexico of sending criminals and rapists across the border and pledged to build a wall that Mexico would pay for if he became president.
He also accused Mexico of cheating the United States on trade.
After their meeting, President Nieto challenged Mr Trump's characterisation of the situation on the US-Mexican border, saying the number of immigrants crossing the border illegally had dropped significantly.
Mr Nieto also said while he was willing to work with either candidate to advance mutual interests, his priority is to defend Mexican people wherever they are.
"I also showed Mr Trump the great responsibility that I have to defend the Mexican population, both to Mexicans who are here and outside of Mexico. That there has been a misinterpretation or assertions that regrettably had hurt and have affected Mexicans."
Many Mexicans, including opposition parties, were furious about Mr Trump's visit, deeply offended by Mr Trump's labelling of Mexicans as rapists and drug traffickers.
Many expected an apology which was not forthcoming.
In California, there have been protests from Latinos, first-time voters and US-born children of immigrants over Donald Trump's immigration policy.
A spokesman for the Coalition for Humane Immigrant Rights of Los Angeles, Jorge Mario Cabrera, says Mr Trump's speech and his meeting with Mexico's president offer no solutions on the issue of illegal immigration.
"While millions of immigrant families in the United States demand real solutions to the illegal immigration issue, to the suffering of millions of Mexicans that have to leave their country because of the lack of jobs, poverty and violence, Donald Trump and President Pena Nieto gives us a circus."
Mr Trump also says if elected, he will form a commission to study which regions or countries he would suspend immigration from, saying Syria and Libya would be high on his list.
It's an amendment to his proposed ban on Muslims that avoids reference to their religious affiliation.
Mr Trump is trailing behind Democratic rival Hillary Clinton in opinion polls for the election on November 8.
