Trump is scheduled to host the lawmakers for lunch on Tuesday, according to his public schedule, which did not say who was attending.

Moderate House Democrats were invited, CNN and Politico reported.

Representatives for the White House and congressional leaders did not immediately respond to a request for comment.

Neither Trump nor Democratic leaders in congress have shown signs of bending on wall funding but the Washington Post on Monday reported a new bipartisan group of US senators is searching for an agreement that could help end the partial shutdown.

Trump, who has demanded $US5.7 billion ($A7.9 billion) from congress to build his long-promised wall along the US-Mexican border, on Monday rejected a call by fellow Republicans to temporarily reopen the government while talks continue on border security issues.

He campaigned in 2016 on a promise of building a wall to stop illegal immigration and drug trafficking, and more recently raised the possibility of declaring a national emergency to go around congress to secure funding for the wall.

In recent days, however, he has said that he would prefer congress to act.

Democrats, who took over the US House of Representatives this month, have rejected the border wall but back other border security measures.

House Democrats have passed a number of bills to fund the roughly one-quarter of federal operations that have been closed, but Senate Majority Leader Mitch McConnell, a Republican, has said the chamber will not consider legislation that Trump will not sign into law.

Senate Democratic leader Chuck Schumer on Monday called on McConnell to move forward, suggesting that congress go around the president.

The partial shutdown is the longest in US history and its effects have begun to reverberate across the country.

Longer lines have formed at some airports as more security screeners fail to show up for work while food and drug inspections have been curtailed and farmers, stung by recent trade spats, have been unable to receive federal aid.

The shutdown began on December 22 and its impact is worrying some on Wall Street. Roughly 800,000 federal employees are feeling the financial sting after missing their first pay cheque last week, a loss of income expected to have ripple effects.

Speaking on CNBC, Delta Air Lines chief executive officer Ed Bastian said the partial shutdown will cost the airline $US25 million in lost revenue in January because fewer government contractors are travelling.

Other US airlines also are not able to open new routes or use new aeroplanes because they need certification from federal officials who are furloughed.

A number of companies, already concerned about a global economic uncertainty, also have urged Republicans and Democrats to end the stalemate in Washington

Australian Associated Press