"We are going to have tremendous border security that will include the wall. A lot of people do not know that we have already started the wall. We have $1.6 billion and we have started large portions of the wall," Trump said on Tuesday as broadcast by the Fox News.
On Sunday, Trump threatened to "shut down" the federal government if Democrats in Congress refuse to support his administration's demands on border security and the wall on the border with Mexico.
The issue of irregular migration has long been a stumbling block in Mexico's relations with the United States, with Trump having repeatedly pledged to build a wall on the southern border in order to stop illegal migration, as well as human and narcotics trafficking.
Building the wall was one of Trump's key pre-election promises.