Democratic and Republican congressional leaders have emerged from a meeting with US President Donald Trump, giving no indication of any progress toward ending a partial government shutdown, now in its 12th day.

House Republican Leader Kevin McCarthy says Trump asked congressional leaders to return to the White House on Friday for more talks, even as the president holds to his demand for $5 billion ($A7 billion) funding for a border wall.

Democrats said they would proceed with plans to hold votes on Thursday, when they formally take control of the House of Representatives from Trump’s Republicans, on legislation that would end the shutdown without providing the wall money sought by Trump.

“We’re asking the president to open up government,” Democrat Nancy Pelosi, the presumptive incoming House speaker, said.

Trump’s demand for funding for a wall along the U.S.-Mexico border triggered the shutdown, affecting about a quarter of the federal government and 800,000 federal workers.

Before meeting with lawmakers, Trump said the shutdown would last for “as long as it takes” as he pushes for wall money – fiercely opposed by Democrats.

“It could be a long time,” Trump told reporters during a Cabinet meeting, “or it could be quickly.”

“We know that we have a challenge along the border,” McCarthy said. “We want to solve that issue. We want to make sure we open this government up. And I think at the end of the day, the president, listening to him, he wants to solve this as well.”

Trump made the border wall a key part of his presidential campaign and has since blamed Democrats for the shutdown.

The $5 billion Trump is seeking would cover only a portion of the money needed for a border wall, a project estimated to cost about $23 billion. Trump had said Mexico would pay for the wall, but Mexico has refused.