President Trump began to edge away Monday evening from demanding that funding for his promised border wall be included in a must-pass spending bill, reducing the chances of a government shutdown at the end of the week by making clear he’s flexible on that timeline.

Trump told a group of 20 conservative media reporters Monday evening that he would be willing to return to the wall funding issue in September, two people in the meeting said. His earlier demand that it be included represented a significant impasse in budget talks, and the latest comments potentially could pave the way for a bipartisan deal just days ahead of the government shutdown deadline.

White House Counselor Kellyanne Conway confirmed to “Fox & Friends” Tuesday morning that the wall does not need to be funded this week, but she said it remains a “very important priority to [Trump].”

“Building that wall and having it funded remains an important priority to him, but we also know that that can happen later this year and into next year,” she said.

Trump also took to Twitter Tuesday morning to make clear that his overall position has not changed.

“Don't let the fake media tell you that I have changed my position on the WALL. It will get built and help stop drugs, human trafficking etc,” he wrote.

Congress is under pressure to pass a $1 trillion spending bill that would pay for government agencies; if the bill fails to pass by midnight Friday, it will trigger a partial government shutdown.

In the wake of Trump’s border wall comments, Senate Minority Leader Chuck Schumer, D-N.Y., welcomed the approach. "It's good for the country that President Trump is taking the wall off the table in these negotiations," Schumer said late Monday. "Now the bipartisan and bicameral negotiators can continue working on the outstanding issues."

House Minority Leader Nancy Pelosi, D-Calif., also praised Trump’s announcement, calling it “welcomed news given the bipartisan opposition to the wall.”

The border wall was the most controversial issue facing lawmakers negotiating the spending bill. Trump insists that Mexico will pay for the wall in the end, a key pledge during his campaign. Cost estimates range past $20 billion, but the White House had been seeking $1.4 billion as a down payment in the spending bill in order to start the process.

Prior to the White House demand late last week for border wall money, it had largely been assumed on Capitol Hill that the spending measure would include funding for additional security steps along the border, but that there wouldn't be any money explicitly dedicated for new wall construction. With the president’s recent comments, that approach now appears likely to prevail.

"I'm optimistic. I don't think anybody wants a shutdown," Sen. Roy Blunt, R-Mo., said as he exited a meeting of GOP leadership. "The White House and basically the minority leaders of the House and Senate have to have some level of agreement on the things that you're adding."

The Associated Press contributed to this report.