"I am in the White House, working hard," the Republican president tweeted Saturday morning. "We are negotiating with the Democrats on desperately needed Border Security (Gangs, Drugs, Human Trafficking & more) but it could be a long stay."

Trump has dug in on his demand for $5 billion for construction of the wall on the US border with Mexico. Democrats are staunchly opposed, and the absence of an elusive deal meant federal funds for dozens of agencies lapsed at midnight Friday.

The House of Representatives and the Senate resumed discussions at noon on Saturday, but the latter chamber adjourned without a deal being reached.

"The Senate will next meet for a pro forma session on Monday, that's the 24th. The next scheduled session day will be on the 27th of December," Majority Leader Mitch McConnell said on the Senate floor.

Top Senate Democrat Chuck Schumer blasted the president and blamed him for provoking the shutdown: "President Trump, if you want to open the government abandon the wall, plain and simple."

"The Trump shutdown isn't over border security; it's because President Trump is demanding billions of dollars for an expensive, ineffective wall that the majority of Americans don't support."

Most critical US security functions remain operational, but 800,000 federal workers are impacted, with many furloughed just days before Christmas while others deemed essential are working unpaid.

And as many other Americans and tourists began their end-of-the year holidays some national parks have shuttered completely, while others remain open but without any visitor services including restrooms and maintenance.

New York's governor provided funding to the Statue of Liberty monument and Ellis Island so those key attractions could remain open.

- 'Dereliction of duty' -

It remains unclear how long the shutdown will last, with Washington unable to accomplish one of its most basic tasks -- keeping the government up and running.

"This is a dereliction of duty by Congress and the president," said David Cox, national president of the American Federation of Government Employees.

Trump's own Republican party still controls both the House and Senate, but in January the House comes under Democratic control.

Governor Ralph Northam of Virginia -- a state bordering the US capital that is home to many federal workers -- urged Trump in a letter Saturday to push immediate action to end the shutdown, saying it "inflicts real harm" on workers.

"I share your desire for strong economic growth throughout the United States, but the current partial government shutdown makes it harder to achieve this goal," the Democratic governor said.

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.

Most NASA employees will be sent home, as will Commerce Department workers and many at the Departments of Homeland Security, Justice, Agriculture and State.

Should they eventually strike a deal, it could swiftly clear Congress and reach the president's desk, said Senate Republican Bob Corker.

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 told AFP.

- 'No agreement' -

But conservatives in the House would likely balk at that figure.

"There's no agreement," congressman Mark Meadows, chairman of the House Freedom Caucus of ultra-conservatives, told reporters as he left a closed-door meeting on the Capitol's Senate side.

"There's a whole lot of numbers being thrown around," but a maximum $1.6 billion for border security "is not acceptable."

Trump reversed course Thursday and 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.

With lawmakers like Meadows and prominent conservative commentators demanding that the president stick to his campaign promises, Trump would not budge on his wall.

The House swiftly passed a bill that fulfilled the president's demands. It included $5.7 billion in wall funding, and $7.8 billion in disaster relief.

But it stalled at the first hurdle in the Senate. (AFP)