As a partial US government shutdown hit the two-week mark, Donald Trump and congressional leaders prepared to meet on Friday to discuss breaking an impasse pitting the president's demand for building a border wall against Democrats' call for alternative security measures.

About 800,000 federal workers have been furloughed or required to work without pay since the partial government shutdown began on December 22.

It remained unclear how much progress might be made during Friday's meeting, which was scheduled for 11:30am (16:30 GMT) in the White House Situation Room, as both Trump and opposition Democrats dug in.

Trump has so far refused to back down from his demand for more than five billion dollars in funding to begin building the wall along the US-Mexico border that he promised during his presidential campaign.

"The president isn't going to back off," White House spokeswoman Sarah Sanders told reporters on Friday morning.

On Wednesday, during a meeting between the president and Democrats, Trump reportedly said he would "look foolish" if he backed away from his demand.

US House Speaker Nancy Pelosi, who took control of the House on Thursday, sought to separate the issue of the wall and government funding, and called on Trump and his fellow Republicans in the Senate to reopen agencies as border talks continue.

"The wall and the government shutdown really have nothing to do with each other," Pelosi, who has rejected any funding for what she has called an "immoral" border wall, said at a Friday event hosted by MSNBC.

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US House Majority Leader Steny Hoye said Democratic congressional leaders hoped to resolve the shutdown at the meeting. "I hope we will open up government," he told MSNBC in a separate interview.

Trump promoted the wall in tweets to keep the pressure on Democrats on Thursday even as they gained significant new power with their takeover of the House of Representatives at the start of a new Congress.

Late on Thursday, the House passed two Democratic bills to immediately reopen government agencies for varying lengths of time, despite a White House veto threat.

Earlier in the day, Senate Majority Leader Mitch McConnell, a Republican, rejected the House effort saying the president would not sign it into law, although the Senate last month approved identical legislation.

Unease among some Republicans

McConnell faces increasing pressure from within his caucus, especially from vulnerable Republicans up for re-election in 2020, as several conservative senators urged action to reopen the government, according to US media.

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"We should pass a continuing resolution to get the government back open. The Senate has done it last Congress, we should do it again today," US Senator Cory Gardner told The Hill on Thursday.

His colleague, Susan Collins, also called for the Senate to pass the funding bills, while several other Republicans urged an end to the shutdown, the Hill and New York Times reported.

Pelosi on Friday urged McConnell to bring the measures up for a vote. "The president can sign or not but he should never say, 'I'm not even going to put it on the president's desk,'" she told MSNBC, noting Congress can pass bills without Trump's support.

Democrats back other border security measures aside from the wall, and their two-bill package passed on Thursday includes $1.3bn for border fencing and $300m for other border security items such as technology and cameras.

Without a deal to end the partial government shutdown, the Department of Homeland Security will not be able to bring some furloughed workers back to their jobs while others continue to be forced to work without paychecks for the time being.

Other federal agencies were also hobbled, including the Justice Department, Commerce Department and departments of Agriculture, Labor, Interior and Treasury.

The partial shutdown also is straining the country's immigration system, worsening backlogs in courts and complicating hiring for employers.

In a December 11 meeting with Pelosi and Democratic Senate Leader Chuck Schumer, Trump said he would be "proud" to shut the government over the security issue and would not blame Democrats. He has since said they are responsible.