Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellPelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Senate GOP aims to confirm Trump court pick by Oct. 29: report Trump argues full Supreme Court needed to settle potential election disputes MORE (R-Ky.) said Thursday that it is "way past time" for Congress to try to get a deal on border security and immigration.

"I think it's way past time, on both sides, that we sit down together and see what we could agree to to improve the situation — not only border security, but also the asylum laws are very challenging," McConnell said.

The GOP leader said it's "way past time for us to have an adult, bipartisan discussion about our immigration laws and see what we can agree to."

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His comments come as President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE has lashed out at Democrats over border security this week, saying in a tweet on Wednesday night that their actions on the issue were "treasonous."

"What the Democrats are doing with the Border is TREASONOUS. Their Open Border mindset is putting our Country at risk. Will not let this happen!" Trump wrote in the tweet.

I think what the Democrats are doing with the Border is TREASONOUS. Their Open Border mindset is putting our Country at risk. Will not let this happen! — Donald J. Trump (@realDonaldTrump) April 10, 2019

Despite the tweet, the White House has been quietly trying to reach out to Democrats to try to see if there is a path forward on immigration legislation.

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McConnell added on Thursday that any immigration legislation should touch on not only border security but also changes to the asylum laws, adding that it would also have to be bipartisan.

The fresh talk about an immigration and border deal comes amid a shake-up at the Department of Homeland Security (DHS) in recent days, which has seen the departure of nearly all senior department officials over the past week.

"It can't all be solved by changing personnel, some of it requires changing the law. That means we have to deal with the Democrats. They're in the majority in the House," McConnell said Thursday.

Some GOP senators, including Homeland Security and Governmental Affairs Committee Chairman Ron Johnson Ronald (Ron) Harold Johnson CIA found Putin 'probably directing' campaign against Biden: report This week: Supreme Court fight over Ginsburg's seat upends Congress's agenda GOP set to release controversial Biden report MORE (Wis.), have floated rolling out new legislation to deal with the asylum law and other migrants detained along the border.

McConnell, asked if he would be reaching out Democrats, predicted that they would see the comments he made Thursday during a pen-and-pad meeting with reporters at the Capitol.

"We talk to each other. And we all read what each other says and I just said how I felt about that," he said.

Asked if he would support opening the discussions up to comprehensive immigration reform — a tall legislative ask in an era of divided government where immigration has been deeply partisan — the GOP leader sidestepped.

"I'm willing to enter into a negotiation to see what we can do to fix the problems," he said.