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".
Ahead of the speech on Tuesday, Vice-President Mike Pence said Mr Trump's decision to address the nation "comes from this president's deep desire to do his job to protect the American people".
Donald Trump says there is a growing crisis along the US-Mexico border that demands immediate and drastic action.
The challenge for Mr Trump is that he has been calling for a wall - a bigger, longer one - since he announced his presidential bid in 2015. That has made it hard for his opponents to believe there is a new situation that requires the same solution, except smaller and shorter.
What's more, administration officials have been vague - perhaps intentionally - on the numbers supporting their claims. They say 4,000 "terrorists" have been caught entering the US, but it turns out most stops happen at airports. There have been only a handful apprehended at the Mexican border (fewer than at the border with Canada).
The White House has recently painted this as a humanitarian problem - and Central American families are, in fact, fleeing poverty and violence. But can he make the case that a wall is the humanitarian answer, and not just a way of making refugee suffering less visible to Americans?
The president must convince a sceptical public that his wall is worth the pain the shutdown is causing government workers and the nation at large.
He has eight minutes on Tuesday to do it.