The president has repeatedly said he could use emergency powers to bypass Congress to unlock the money, a move which would be fiercely opposed by Democrats and could thrust the country into a constitutional crisis.
The federal government has been in partial shutdown for 17 days amid an impasse over the $5.6 billion wall, which Mr Trump claims is needed to stop immigrants crossing the country’s southern frontier.
Democrats have refused to sign off a spending bill that would fund the project, which was a cornerstone of the president’s 2016 election campaign.
Mr Trump told reporters at Camp David on Sunday he may declare a national emergency “depending on what happens over the next few days”.
“We can call a national emergency because of the security of our country, absolutely,” he said at another press conference at the White House on Friday, when he suggested he could use military funding to pay for the construction of the wall.
On Monday, Mr Trump tweeted that he was keen to “get our deal done in congress”. But he also quoted Democrat congressman Adam Smith, the new chair of the House Armed Services Committee, who told ABC News that the president “can declare an emergency. It’s been done a number of times.”
However, president’s tweet omitted the full context of Mr Smith’s quotes, which stressed he would be “wide open to a court challenge” if he attempted to use emergency powers to force through the border wall.
Asked if Mr Trump had the authority to call declare a national emergency over border security, the congressman told This Week: “Unfortunately, the short answer is yes. There is a provision in law that says the president can declare an emergency. It’s been done a number of times.
“But primarily it’s been done to build facilities in Afghanistan and Iraq. In this case, I think the president would be wide open to a court challenge saying, ‘where is the emergency?’ You have to establish that in order to do this. But beyond that, this would be a terrible use of Department of Defence dollars.”
Adam Schiff, Democratic leader of the House Intelligence Committee, dismissed Mr Trump’s threat to use emergency powers was “a non-starter”.
He told CNN on Sunday: “If Harry Truman couldn’t nationalise the steel industry during wartime, this president doesn’t have the power to declare an emergency and build a multi-billion dollar wall on the border. So that’s a non-starter.”
Legal experts have also suggested deploying the military to build the wall could be illegal.
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Bruce Ackerman, a professor of law at Yale, said the US constitutional tradition “profoundly opposed” the president using the military to enforce domestic law.
On Sunday, Democratic congresswoman Alexandria Ocasio-Cortez compared Mr Trump's demands for a border wall to "hostage taking".
Her comments came after the president threatened to keep the the partial government shutdown going for “months, or even years," despite more than 800,000 public workers going unpaid for weeks.
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