Operations for several key agencies ceased at 12:01 a.m. Saturday (0501 GMT), despite last-ditch talks that continued on Capitol Hill between White House officials and congressional leaders in both parties, AFP reported.
While most critical security functions remain operational, the effects of the budget wrangling and uncertainty have cast an air of chaos over the capital, which is also reeling from Defense Secretary Jim Mattis's resignation announcement on Thursday.
The uncertainty pushed Wall Street into a third straight rout on Friday, to end its worst week since late 2008 at the start of the global financial crisis.
"President Trump threw a temper tantrum and convinced House Republicans to push our nation into a destructive Trump Shutdown," Chuck Schumer, the top opposition Democrat in the Senate, and his House counterpart, fellow Democrat Nancy Pelosi, said in a joint statement.
Trump has dug in on his demand for $5 billion for construction of a wall to curb illegal immigration on the US border with Mexico. Democrats are staunchly opposed, and the absence of an elusive deal means federal funds for dozens of agencies lapsed at midnight Friday.
The House of Representatives and the Senate are due back in session at noon on Saturday but it remains unclear how long the shutdown – the third this year – will last.
Trump expressed hope late Friday night that it "will not last long," after earlier saying he was ready for just that.
His own Republican party still controls both the House and Senate, but that will change in January when the House comes under Democratic control.
For now, 800,000 federal employees will be either furloughed or forced to work without pay in the run-up to the Christmas holiday.
"The failure to fund the government's operation is shameful, unacceptable, and a completely avoidable waste of taxpayer dollars," David Cox, national president of the American Federation of Government Employees, said in a statement.
"This is a dereliction of duty by Congress and the president."
But the prospect of a large portion of government workers going without paychecks was not enough to spur lawmakers or the president to action.
The House of Representatives adjourned just before 7:00 p.m. Friday, with no moves taken to avert a shutdown, and the Senate closed up shop an hour later.
About three-quarters of the government, including the military and the Department of Health and Human Services, is fully funded until the end of September 2019, leaving 25 percent unfunded as of Saturday.
"It's up to the Democrats whether or not we have a shutdown tonight," Trump said earlier Friday, blaming his political opponents for the crisis.
"I hope we don't," the president added, but "we're totally prepared for a very long shutdown."
Senators told reporters that congressional leaders from both parties were negotiating behind the scenes with White House officials including Vice President Mike Pence, Trump's son-in-law Jared Kushner, and incoming chief of staff Mick Mulvaney.
One focus of discussion was the $1.6 billion in border security funding that was a part of pending Senate legislation, number two Senate Republican John Cornyn said.
Trump Thursday rejected a measure that had unanimously passed the Senate and was under House consideration.
It would have extended government funding until February 8, but contained no money for a border wall, a pet project Trump has fought for since his presidential campaign.
Democrats painted Trump as the Grinch who stole the year-end deal.