WASHINGTON, Jan. 2 (Xinhua) -- Senate Majority Leader Mitch McConnell said Wednesday that the partial government shutdown could continue for days or even weeks due to continued discrepancy between the Congress and the president.

"I don't think any particular progress was made today, but we talked about all aspects of it. It was a civil discussion," McConnell told reporters after a White House meeting with President Donald Trump and other congressional leaders.

Homeland Security Department officials also joined the meeting, or the "briefing" on border security, the first time the president sat down with top congressional leaders of both parties since the start of the shutdown, which has stretched into its 12th day.

"We're hopeful that somehow in the coming days and weeks we'll be able to reach an agreement," McConnell said.

The House Democrats plan on moving forward with spending bills to reopen the government Thursday, when they take control of the lower chamber. That includes measures to keep the Homeland Security Department funded at the current level until Feb. 8, and to fund the eight other cabinet departments affected by the shutdown through Sept. 30, the end of the fiscal year.

Senate Democratic Leader Chuck Schumer said he challenged the president to give one reason why he would continue the shutdown. "He could not give a good answer," he told reporters after the meeting.

"So we would hope that they would reconsider and would support the very bills that pass the Senate, open up the government as we continue to debate what is the best way to secure our border," Schumer said.

Trump, meanwhile, showed no willingness to back down from his original demand. When asked by a reporter at a cabinet meeting Wednesday morning whether he would accept a bill containing border wall funding below 5 billion U.S. dollars, the president said "I'd rather not say it."

"The 5 billion dollars approved by the House is such a small amount compared to the level of the problem," he said, referring to the 5.7 billion dollars for border wall funding approved by the Republican-controlled House on Dec. 20. The bill failed to garner enough votes from the Senate on the following day, leading to the partial government shutdown.

Trump had also rejected an earlier offer by Vice President Mike Pence to accept 2.5 billion dollars for the wall, which was made when Pence and other top officials met with Schumer at the start of the shutdown.

The shutdown, which affected a quarter of the federal government, has forced about 420,000 federal employees, who are deemed essential, to work without pay, while 380,000 others are expected to take unpaid leave.