"Second meeting set for tomorrow", Trump tweeted.
"I can relate", Trump told the reporter before attempting to reassure her that Americans suffering from the shutdown would find a way to cope.
The standoff has prompted economic jitters and anxiety among some in Trump's own party.
Meanwhile, Mick Mulvaney, his acting chief of staff, said the United States president was prepared to take the notion of a concrete wall permanently "off the table" replacing it with a "steel fence" as a concession to Democrats.
"I don't call it a shutdown".
"I don't like doing this, I have no fun doing this, I was elected to protect our country, that's what I'm doing", he said.
He also signalled a possibility of using emergency powers to build the wall without congressional approval and necessary funds.
Showing little empathy for the hundreds of thousands of federal workers told to stay away from work or working without pay, Mr Trump declared - without citing evidence - that most are Democrats.
"I'm not saying their whole plan is a valid plan, but I see no reason why the bills that are ready to go and on which we've achieved an agreement should be held hostage to this debate over border security", Collins said Thursday, per The Washington Post. "Let's get those [departments] reopened while negotiations continue".
Mulvaney, in an interview with NBC's "Meet the Press", said Trump was considering accepting funding to build a steel fence, despite his campaign promise that the wall be built of concrete.
Mr Trump is demanding that any funding to keep the federal government operational also include $5.6 billion to begin building a $23 billion a wall along the USA border with Mexico.
Trump has demanded Congress appropriate money for the wall, and his dispute with Democrats over the issue pushed the government into an ongoing partial shutdown.
Newly sworn-in Rep. Rashida Tlaib (D-Mich.) said that she was not backing down from a vulgar comment she made about impeaching President Donald Trump, but she sang a different tune when challenged by reporters.
Democrats have offered Trump $1.3 billion in new funding for border security, but not for a wall, which they say is an immoral, ineffective way of controlling border access to thwart illegal immigration.
Pence did not have the President's blessing to float new or specific numbers as he did last month in a meeting with Senate Minority Leader Charles Schumer, according to two Trump aides.
Trump threatened again, without providing specifics on where the funding would originate, to declare a national emergency as an alternative way to build the wall, depending on the outcome of talks in the coming days.
Some GOP senators up for re-election in 2020, including Cory Gardner of Colorado and Susan Collins of ME, have voiced discomfort with the shutdown in recent days.
"An all concrete Wall was NEVER ABANDONED, as has been reported by the media".
Trump was joined by Pence in the Rose Garden, as well as House Republican leaders Kevin McCarthy and Steve Scalise.
The meeting comes one day after Vice President Mike Pence, top White House officials and senior congressional aides emerged empty-handed after more than two hours of negotiations on ending the stalemate.
House Armed Services Committee Chairman Adam Smith, meanwhile, said that while the president does have the authority to declare an emergency, any move toward that end would leave the administration "wide open" to a court challenge. "And Senate Republicans are just the right ones to intervene".
The shutdown has left transportation security agents and Federal Bureau of Investigation employees, among many others, working without pay.
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