"I can't tell you when the government is going to be open", the Republican president told reporters at the White House after his annual Christmas teleconference with U.S. troops.
The president said Tuesday, he wanted to be with his family for Christmas, who were in Florida.
"Whatever it takes", he told reporters accompanying him Wednesday on an unannounced visit to US troops deployed at an air base in Iraq.
A spokesperson for House Minority Leader Nancy Pelosi said Democrats' likely plan is to put a bill that funds the government, without money for Trump's wall, on the floor on January 3.
Trump made these remarks while taking questions from reporters during a briefing with United States military leaders shortly after landing in Iraq.
People walk up the steps even though the National Archives is closed with the partial government shutdown in Washington. He now regrets going against his instincts previous year when he approved a plan to send thousands more troops to Afghanistan at the urging of foreign policy advisers, said a person familiar with the process. "We need safety for our country", Mr. Trump told reporters after meeting with USA service members in Iraq on Wednesday.
In a nod to the political stakes he's facing, the president said he wants the wall by "election time" in 2020.
Lawmakers are away from Washington for the holidays and have been told they will get 24 hours' notice before having to return for a vote. Workers are not paid in full while on leave, though are customarily compensated with backdated pay once the shutdown is over.
Trump claimed on Monday that federal workers are behind him in the shutdown fight, saying many "have said to me and communicated, 'stay out until you get the funding for the wall.'" He didn't say who he had heard from.
With Democrats taking control of the House next month, Trump sees this as his last likely chance to secure funding for the border wall, fulfilling one of his most crucial promises of the campaign, his advisers say.
Since the shutdown fell over the weekend, and Monday and Tuesday were federal holidays, most government employees haven't felt the effects yet.
Senate Democratic leader Chuck Schumer of NY suggested that the president's insistence on a wall IS little more than an attempt to mollify his political base.
Democrats have supported including an additional US$1.3 billion in border security funding, at one point agreeing to an additional US$1.6 billion during negotiations with congressional Republicans.
The president appeared to be trying to use his unprovoked attack on Comey as a way of highlighting supposedly unpredictable behavior from the Democratic party that has led to the current government shutdown.
Trump declined to say whether he would accept $2 billion for new fencing, as is said to have proposed to Schumer. "It wasn't really (nerve-wracking), I just had to think of what the truth was".