US President Donald Trump has forced the cancellation of a trip to Afghanistan by his Democratic opponent Nancy Pelosi, and scrapped administration officials' travel to the Davos forum as a government shutdown plunged Washington deeper into deadlock.

The mess in the US capital already verged on the surreal as Congress feuds with the White House over how to end an impasse now in its fourth week, with thousands of federal workers left unpaid.

But now it is also getting increasingly personal between the two main antagonists.

In a letter laced with sarcasm, Mr Trump told House Speaker Nancy Pelosi: "I am sorry to inform you that your trip to Brussels, Egypt, and Afghanistan has been postponed. We will reschedule this seven-day excursion when the Shutdown is over."

"I am sure you would agree that postponing this public relations event is appropriate," he wrote.

And in a move that appeared aimed at heading off Democratic criticism about non-essential administration travel during the shutdown, the White House announced the cancellation of a trip to the World Economic Forum by Treasury Secretary Steven Mnuchin and others "out of consideration for the 800,000 great American workers not receiving pay".

Mrs Pelosi and her delegation had planned a non-publicised trip to Afghanistan - an active war zone - and were due to travel aboard a US Air Force plane. Her office said Egypt was not on the itinerary.

According to a congressional aide, several politicians were already loaded onto buses preparing to leave the US Capitol when Mr Trump pulled the plug.

Mr Trump also said that Mrs Pelosi could still book her own non-government flights.

"Obviously, if you would like to make your journey by flying commercial, that would certainly be your prerogative," he wrote.

The cancellation followed Mrs Pelosi's suggestion that President Trump postpone his 29 January State of the Union address to Congress, or do it from the White House instead.

Although she cited the shutdown's effect on security, she appeared to want to deny the president one of his chief annual moments in the limelight.

The White House denied that the travel blockage was payback, but few bought the argument.

House Democrats, who had been set to go on the trip were left fuming, including new congresswoman Elaine Luria, a 20-year Navy veteran who said the purpose was to express appreciation to Americans in uniform and gain critical intelligence on the ground.

"Oversight is the responsibility of Congress, and it is inappropriate for the President to interfere with our constitutional duties," Ms Luria said in a statement.

Republican Senator Lindsey Graham, who for weeks has served as a referee of sorts between Mr Trump and Mrs Pelosi, accused the latter of "playing politics with the State of the Union".

But he also hit out at Mr Trump, saying "denying Speaker Pelosi military travel to visit our troops in Afghanistan, our allies in Egypt and NATO is also inappropriate".

"One sophomoric response does not deserve another," Mr Graham added.

The government shutdown is due to Mr Trump's refusal to sign off on funding for a host of departments, in retaliation for the Democratic-led House's refusal to approve his US-Mexico border wall project.

The shutdown is leaving an increasingly deep impact across the country, where for almost a month FBI agents, museum workers, US Coast Guard personnel and other officials have been either ordered to stay home or forced to work without pay.

Federal workers queue for food and coffee during the shutdown

Regular employees will get back pay eventually, while contractors will not.

The Democrats and the White House blame each other for the impasse, with neither side showing signs of backing down.

Trump critics quickly pointed out that he himself visited troops in Iraq during the shutdown.

House Intelligence Committee chairman Adam Schiff said he believed cancelling a speaker of the House's fact-finding mission to a war zone was a first for a US president.

"We believe this is completely inappropriate by the president. We're not going to allow the President of the United States to tell the Congress it can't fulfill its oversight responsibilities, it can't ensure that our troops have what they need whether our government is open or closed," he told reporters.

"That work must go on and I think it's vitally important now, in particular that the president has announced withdrawals from Syria and Afghanistan, that we understand the situation on the ground."