He said he hoped Democrats would work with Republicans in"good faith"to secure a barrier on the border that would stop immigrants and drugs coming into the US illegally.
"We really have no choice but to build a powerful wall or steel barrier,"he said.
"If we don't get a fair deal from Congress,the government will either shut down on Feb. 15,again,or I will use the powers afforded to me under the laws and the Constitution of the United States to address this emergency.
"We will have great security."
Referring to the possibility of declaring a national emergency,Trump said he had a"powerful alternative"at his disposal but that he had not wanted to use it.
Trump expressed gratitude for federal workers who had gone without pay during the shutdown.
"I will make sure that all employees receive their backpay very quickly or as soon as possible,"he said.
"It'll happen fast."
The Democrats'leader in the Senate,Chuck Schumer,said:"Hopefully now the President has learnt his lesson.
"We cannot hold the American people hostage ever again."
A new poll byThe Washington Post and ABC found that Trump's popularity had weakened during the shutdown,with 37 per cent of the public approving of his job performance and 58 per cent disapproving.
Trump's backdown angered vocal members of his conservative base,who have insisted he must do whatever it takes to build a wall.
"Good news for George Herbert Walker Bush:As of today,he is no longer the biggest wimp ever to serve as President of the United States,"tweeted right-wing commentator Ann Coulter.
Trump's announcement came just hours afterspecial counsel Robert Mueller indicted one of the president's longtime allies,Roger Stone,on seven criminal charges.
These included lying to Congress,witness tampering and obstruction.