By Jeff Mason and Amanda Becker

WASHINGTON (Reuters) - A meeting between U.S. congressional leaders and President Donald Trump on Wednesday yielded no sign of an agreement to end a partial government shutdown now in its 12th day as the president stuck to his demand for $5 billion in funding for a border wall.

Congressional leaders are expected to return to the White House on Friday to resume talks, signaling the shutdown will likely stretch into the weekend.

The White House had convened the meeting to try to convince Democrats that funding a wall on the southern border with Mexico was a pressing security need. Instead, Democratic leaders cut off Homeland Security Secretary Kirstjen Neilsen's presentation and tried to no avail to press Trump to accept their offer.

"It just was not a credible presentation," Senator Dick Durbin said of the briefing. He added that Senate Minority Leader Chuck Schumer and Nancy Pelosi, who is expected to be elected House speaker on Thursday, insisted the conversation focus instead on the shutdown.

Pelosi said the House would proceed with plans to hold votes on Thursday, when they formally take control of the chamber from Trump's fellow Republicans, on legislation that would end the shutdown without providing the wall money sought by Trump. The White House has called the two-part package a "non-starter."

"We're asking the president to open up government," Pelosi told reporters outside the White House after the meeting.

Democrats say they want to fund most of the government through September, but allow for another month to negotiate wall funding by only partially funding the Department of Homeland Security, which is responsible for the wall.

Schumer said Trump conceded that Republicans would lose leverage if they allowed the rest of the government to be funded.

"We asked him to give us one good reason ... why you should continue your shutdown of the eight Cabinet departments while we are debating our differences on homeland security. He could not give a good answer," Schumer told reporters after the meeting.

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'AS LONG AS IT TAKES'

Trump's demand for $5 billion in 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 - as part of any legislation to reopen agencies shuttered when their funding lapsed on Dec. 22.

"It could be a long time," Trump told reporters on Wednesday during a Cabinet meeting, "or it could be quickly."

"We know that we have a challenge along the border," said Kevin McCarthy, the top House Republican. "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's meeting with lawmakers was held in the White House Situation Room, generally used for high-level security concerns such as military planning.

Pelosi noted that the legislation being presented in the House had previously won backing in the Senate, which will remain in Republican hands in the new 2019-2020 Congress that convenes on Thursday.

Republican Senate Majority Leader Mitch McConnell has said Senate Republicans will not approve a spending measure Trump does not support.

Trump made the border wall a key part of his presidential campaign. Before meeting with the Democrats, Trump called the border a "sieve," rebutted Pelosi's complaint that a wall was immoral, provided an estimate of the U.S. illegal immigrant population far higher than the figures most experts cite and made disputed comments about progress toward building a wall.

The visit by Pelosi and Schumer was their first to the White House since their sharp exchange with Trump in the Oval Office on Dec. 11 during which the president told them he would be "proud to shut down the government for border security."

He 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.

(Reporting by Jeff Mason and Amanda Becker; Additional reporting by Doina Chiacu and Susan Cornwell; Writing by Will Dunham and Ginger Gibson; Editing by Bill Trott and Peter Cooney)