"I call it doing what you have to do for the benefit and the safety of our country", he added.
"If he has to give up a concrete wall, replace it with a steel fence to do that so that Democrats can say, 'See? It may be better", he said.
Following the meeting, Trump doubled down on his border wall demand and said he had designated Vice President Mike Pence, Homeland Security Secretary Kirstjen Nielsen and adviser Jared Kushner to lead the weekend negotiations.
Mulvaney said that Trump would "take a concrete wall off the table" in negotiations with Democratic leaders if that would help end the shutdown. "V.P. Mike Pence and team just left the White House".
"It'll be discussed", he said on NBC.More news: Cleveland Browns: Studs and duds from season finale loss against Ravens
Trump, in his comments to reporters Sunday morning, said he and Pence did not "expect to have anything happen" at further shutdown talks between Pence and congressional leadership staff Sunday afternoon. It's been done a number of times but primarily it's been done to build facilities in Afghanistan and Iraq and in this case, I think the president would be wide open to a court challenge, saying 'where's the emergency?'" Smith told George Stephanopoulos on "This Week" on Sunday "You have to establish that in order to do this.
CNN host Jake Tapper pressed acting White House Chief of Staff Mick Mulvaney on Donald Trump's boast on Friday that he has been receiving calls from former presidents who support his wall - only to haveMulvaney simultaneously duck the question while blaming Senate Minority Leader Chuck Schumer (D-NY) for it.
Employees of the Transportation Security Administration are expected to work without pay during the shutdown because their jobs are considered essential.
People familiar with the session but not authorized to speak publicly described Trump as holding forth at length on a range of subjects but said he made clear he was firm in his demand for $5.6 billion in wall funding and in rejecting the Democrats' request to reopen the government.
Trump has asserted that he could relate to the plight of the hundreds of thousands of federal workers going without paychecks for the moment, though he acknowledged they would have to "make adjustments" to deal with the shutdown shortfall.More news: LeBron James, Lonzo Ball lead Lakers in All-Star voting
"Everybody's playing games, but I can say this, I think that the Democrats want to make a deal", Trump said. "I don't know what he's basing this on, but he's faced so many lawsuits when he ignores the law and ignores tradition and precedent", Durbin said on CBS' "Face the Nation".
The Republicans had passed an initial funding bill including $5bn (£4bn) for the wall, when they still had a majority in the House, but they could not get the necessary 60 votes in the 100-seat Senate.
Pelosi said that she has a "generational" reaction to that language and wouldn't use it, but that she won't censor her colleagues.
House Democrats plan to pass a series of bills this week to reopen government, breaking up legislation they have already approved in a bid to get Republicans to agree to reopen certain agencies, Hoyer said on "Meet the Press".
The White House switchboard and the call-in phone line to the White House are not operating due to the government shutdown, so it is unclear what calls he is referring to, of if any such calls actually occurred. "Not the other way around", he said.More news: Tesla cuts prices as 4Q deliveries miss analysts' estimates