Mr Trump will make his case in his first speech from the Oval Office at 21:00EST (0200 GMT Wednesday), ahead of a trip to the border on Thursday.
A partial government shutdown has been in effect for 17 days after lawmakers failed to break a budget impasse.
The president is insisting that $5bn (£4bn) be included for the border wall.
White House press secretary Sarah Huckabee Sanders said in a tweet that Mr Trump would use his visit to the border on Thursday to "meet with those on the front lines of the national security and humanitarian crisis".
