Video report by ITV News Washington Correspondent Robert Moore
Donald Trump has promised to make Mexico pay for an "impenetrable and beautiful" wall between the two countries.
Speaking after a meeting with the Mexican president on Wednesday, the Republican presidential candidate said building a wall would start on day one of his presidency.
Mr Trump vowed Mexico would pay "100%" for the wall, despite Mexico's Enrique Pena Nieto saying he made clear his country would not fund it when he met the billionaire.
The Republican nominee told a rally in Arizona he would overhaul the US's immigration system, threatening millions of undocumented immigrants with deportation.
Setting out his 10-point plan, Trump said he would focus particularly on blocking immigrants from Syria and Libya.
Speaking of a "special and important" meeting with Mexico's Enrique Pena Nieto, Trump said the pair had discussed ending the illegal flow of "drugs, cash, guns and people" across the Mexican-US border.
But even though "they don't know it yet", the Mexicans would pay for the 2,000-mile construction across the US's south border "100%".
At an emotional rally in Phoenix, Arizona, Trump told the chanting crowd: "We will build a great wall along the southern border... and Mexico will pay for the wall. 100%.
"They don't know it yet but they are going to pay for the wall".
Amid chants of "build a wall", Trump told the crowd the construction would be an "impenetrable, physical, tall, powerful, beautiful, southern border wall".
Speaking of his plans for immigration into the US, the Republican said he would beef up deportation agencies and restrict immigrants from places where "adequate screening" was not possible.
Immigrants from Syria and Libya would be impacted in particular and vetting would be "extreme", he warned.
"We also have to be honest about the fact, that not everyone who seeks to join our country will be able to successfully assimilate", Trump said.
"It is our right as a sovereign nation to choose immigrants that we think are the likeliest to thrive and flourish and love us".
Trump added that the 11 million illegal immigrants in America would have to return home and re-apply for re-entry.
Trump said he expected the meeting with Mexico's president to be the first of "many, many" conversations been the two countries as they "go about creating a new relationship".
But that would be a "fair relationship", he added.
Trump's plans for immigration into the US
Create new deportation task force
Triple number of immigration and customs enforcement agents
Suspend visas to any place "where adequate screening cannot occur"
Impose "ideological certification" for immigrants seeking to enter US
Determine regions or countries from where immigration to the US should be suspended
Focus on blocking refugees from Syria and Libya
Undocumented immigrants must leave and apply to return legally
Undocumented immigrants cannot obtain legal status or citizenship by entering country illegally