A partial US government shutdown has taken effect after US lawmakers failed to break a budget impasse.
Mr Trump, who has to sign off any deal, is insisting at least $5bn (£4bn) in funding be included for his long-promised wall along the Mexican border.
Lawmakers adjourned last-minute talks on Friday evening.
In the absence of an agreement, funding for about a quarter of all US federal agencies lapsed at midnight (05:00 GMT Saturday).
It means the departments of Homeland Security, Transportation, Agriculture, State, and Justice will begin to shut down and federal national parks and forests will also close.
The partial closure, the third of 2018, means hundreds of thousands of federal employees will have to work unpaid or be put on temporary leave.
In a video address published on Mr Trump’s Twitter account shortly before the shutdown began, the president insisted the onus was on the Democrats to resolve the closure.
Senior Democrats have accused the president of provoking the situation with a “temper tantrum”.
On Wednesday, a stopgap spending bill was passed in order to keep federal agencies open until 8 February – but the agreement did not include funding for Mr Trump’s wall.
After a rare backlash from his supporters and hard-line Republicans, Mr Trump dug his heels in over the issue and insisted funds for the wall must be included for him to sign it off.
Under current rules, spending bills are approved in the House of Representatives with a simple majority vote. Mr Trump’s party currently dominate that chamber, but the Democrats are set to take control of it in January.
The House has now approved $5.7bn (£4.5bn) of funding for the wall, but before the spending bill reaches the president it also needs to be passed by 60 votes in the Senate – where Republicans only hold 51 seats.
On Friday Mr Trump shared a graphic of his steel-slat wall design for the wall.
Later, he posted a video regarding the immigration row, where he said it was “very dangerous out there”.
His address, which was spliced with footage that appeared to show immigrants pushing down border fencing, cautioned about drugs and violent gang members entering the country illegally.
“We don’t want ’em in the United States, We don’t want ’em in our country,” Mr Trump said.
“The only thing that’s going to stop that is great border security with a wall, or a slat fence, or whatever you wanna call it.”