A committee of Republican and Democrat politicians would be formed to consider border spending before the new deadline.
The president also suggested he was still considering taking unilateral action by declaring a national emergency, which would allow him to use the Pentagon budget to build the wall. However, that would face legal challenges.
Mr Trump said: “I have a very powerful alternative, but I didn’t want to use it at this time.
“They [The Democrats] are willing to put partisanship aside, I think, and put the security of the American people first. We really have no choice but to build a powerful wall or steel barrier.
“If we don’t get a fair deal from Congress, the government will either shut down on February 15, or I will use the powers afforded to me under the laws and Constitution of the United States to address this emergency.”
On Thursday night at least five Republican senators had called on the president to reopen the government.