He told a cheering crowd in Arizona that he would secure the border, and left open the possibility that millions of illegal immigrants be deported.
Hours earlier, he met the Mexican President Pena Nieto but said they did not discuss who would pay for the wall.
The president later insisted he had told Mr Trump Mexico would not pay.
There had been speculation that the Republican candidate would back off his plan to deport the estimated 11m undocumented immigrants living in the US.
