"It was a civil discussion. We're hopeful that somehow in the coming days and weeks we'll be able to reach an agreement," McConnell told reporters, opening the door to a lengthy shutdown that is already in its 12th day.

McConnell and other members of congressional leadership of both parties met with Trump and members of the Department of Homeland Security (DHS) for what was billed as a "briefing" on the border.

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But lawmakers say that was quickly derailed with Republicans accusing Democrats of interrupting and Democrats stressed their time would be better spent talking about the partial shutdown.

McConnell added that they had a "good discussion" on border security but acknowledged they had not yet found a way to break the stalemate over Trump's U.S-Mexico border wall.

"I don't think any particular progress was made today, but we talked about all aspects of it. It was a civil discussion," he said.

The shutdown began Dec. 22 after Democrats refused to agree to Trump's demand for $5 billion in funding for a wall on the Mexican border.

House Democrats are expected to vote on Thursday on a package to reopen the government. One bill would fund DHS through Feb. 8. The second would fund the remaining six bills through Sept. 30, the end of the 2019 fiscal year.

But the White House and Senate Republicans have vowed not to move the bill once it reaches the Senate.

"As I've said for the last two weeks, the Senate will be glad to vote on a measure that the House passes that the president will sign. But we're not going to vote on anything else," McConnell said.

Asked if that meant he won't take up the House bill, he added: "That's right."