"Either we build (finish) the Wall or we close the Border," the US president tweeted after nearly a week of deadlock in Washington over the federal budget.
Confirming the threat to close the border was real, the White House said negotiations with Congress had stalled.
The dispute has caused a partial US government shutdown.
Hundreds of thousands of federal employees are either on unpaid leave or continue to work but do not know when they will be paid.
Both Congress chambers met for just a few minutes on Thursday but took no steps to end the closure. The House and Senate will now meet again on Monday.
Later in the week, a new House will be sworn in, dominated by opposition Democrats who won the mid-term elections last month, but Mr Trump's Republicans will retain the Senate with a slightly larger majority.
In October Mr Trump made a similar threat to close the southern US border when demanding action from Latin American governments to stop migrants, in what has become known as the caravan, trying to cross into the US illegally.
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