Washington CNN  — 

Senate Majority Leader Mitch McConnell – who argued publicly this week that he has a limited role to play in resolving the standoff over government funding – was notably absent from a news conference with President Donald Trump Friday that followed his high-stakes meeting with congressional leaders to discuss the ongoing government shutdown.

While McConnell and Sen. John Thune, a South Dakota Republican and his new deputy in Senate GOP leadership, left the White House after the meeting, House Minority Leader Kevin McCarthy and Whip Steve Scalise stood behind Trump in the Rose Garden as the President boasted during a lengthy and far-reaching session with reporters that he could “call a national emergency” to build a border wall with Mexico – the issue at the center of the shutdown stalemate – without the approval of Congress if he wants, and defended the use of eminent domain, something that is unpopular with many conservatives, to facilitate construction.

At one point, a reporter explicitly asked the President, “Why is Senator Mitch McConnell not here? Why was he not invited to this?”

Trump replied that McConnell was not there “because he’s running the Senate,” despite the fact that the Senate adjourned for the weekend before the White House meeting started and will not be back in session until Tuesday.

The President also praised the Senate GOP leader, saying, “He’s been great. He’s been really fantastic.”

Trump also emphasized that McConnell had been at the meeting. “He was here. He was with us for hours at the meeting.”

Don Stewart, a spokesman for McConnell, told CNN that the two Republican senators left the White House after the meeting unaware a press conference was planned. They would have attended if asked, Stewart said.

McConnell told CNN on Thursday that he has not been “sidelined” in talks to reopen parts of the government, but asserted that he has “no particular role” to play in ending the standoff, a responsibility he argued falls to the President and congressional Democrats who wield expanded power in the new Congress now that Democrats have taken over the House majority.

The Senate majority leader did speak to reporters at the Capitol on Friday as he returned from the meeting at the White House, saying that it was a “spirited discussion as you can imagine.”

“I would say the news is that the President agreed to designate his top people to sit down with all the leaders’ staffs this weekend to see if we can come up an agreement to recommend back to us, the various leaders,” McConnell said.

He added that “the government couldn’t reopen until Tuesday anyhow because we don’t have people here to vote” since both chambers of Congress gaveled out of session on Friday and won’t return until Tuesday.

How McConnell is handling the government shutdown fight

In recent days, McConnell has kept a relatively low-profile in the midst of the shutdown fight and distanced himself from negotiations to end the impasse.

McConnell had opposed shutting down the government, and in late December, it seemed briefly that a partial shutdown would be averted when Senate Republicans and Democrats joined together to pass a stop-gap funding bill that would have prevented a shuttering of roughly a quarter of the federal government.

When the Senate passed the measure, the proposal had the backing of congressional Democratic leaders and top congressional Republicans had indicated they were optimistic the President would sign it.

But the plan was upended a day later when it came time for the House to take up the legislation. After facing criticism from conservative allies who wanted to see him push for border wall funding, the President abruptly informed House GOP leaders that he would not sign the bill because it did not match up with his demands for the wall.

In a brief hallway interview on Thursday, McConnell explained that his role is now reversed from when he and then-Vice President Joe Biden worked to avoid a fiscal cliff and negotiated other tough issues during the Obama administration.

“Well, it’s not complicated. I was in this role when Obama was President, and Biden and I did deals because they needed some of our votes. So, now the role is reversed and ultimately the solution to this is a deal between the President and Nancy and Chuck because we need some of Chuck’s votes and obviously we need Nancy’s support,” he said, referring to newly installed House Speaker Nancy Pelosi of California and Senate Minority Leader Chuck Schumer, a New York Democrat.

“So, I haven’t been sidelined,” McConnell added. “It’s just that there’s no particular role for me when you have this setup.”

CNN’s Manu Raju contributed to this report.