Speaking from the Rose Garden at the White House, Trump said: "I am proud to announce we have reached a deal to re-open the government". Trump has threatened to veto legislation that doesn't include wall funding.
White House spokeswoman Sarah Sanders said a temporary measure to reopen shuttered government departments and agencies must have "a large down payment on the wall". Prospects for a compromise are dim, as a tit-for-tat battle between Trump and House Speaker Nancy Pelosi has been escalating.
Media captionOther presidents got money for a border barrier - why not Trump?
"I have other alternatives if I have to and I'll use those alternatives if I have to", the President said on Thursday.
The proposal would provide up to $5.7 billion to boost personnel at the border, add technical enhancements like sensors and drones and more immigration judges. But in a sign of cracks in that resolve or a desire for compromise, six Republican senators voted with Democrats on their measure to temporarily reopen government agencies without money for Trump's wall.
With no signs of compromise on the standoff over funding for a border wall, new polls found that after 34 days of government shutdown, Americans are growing exhausted of the deadlock and want an agreement reached as soon as possible.
McConnell said late on Thursday that talks were ongoing.
United States lawmakers and the White House faced intensifying pressure Friday to resolve a five-week impasse and reopen government, as the political stalemate has begun to affect the nation's busy airports.
Republican Sens. Susan Collins of ME and Cory Gardner of Colorado said they would vote for both proposals in the procedural vote Thursday. "But we can't do it with the government shut down".
In a sign, however, that Americans overall are willing to support any kind of agreement to get the government fully running again, 66 percent said Trump should agree to a bill with no wall funding and 52 percent overall said that Democrats should agree to a deal which included wall funding. "The second proposal is something we all voted for before". It would mark a significant win for House Democrats, despite Trump saying Republicans would not "cave" just a day earlier.
The Republican President has been forced to postpone his State of the Union speech, scheduled for next Tuesday at the Congress, at the request of Nancy Pelosi who had withdrawn her invitation for security issues related to "shutdown", according to her.
Most Democrats oppose direct funds for wall construction, but some have begun publicly advocating for negotiating a solution that includes boosted border funding, including for border structures.
The pain inflicted by the shutdown is "getting deeper and deeper every day", with 800,000 federal employees set to miss another paycheck on Friday, Schumer said.
Trump's proposal, however, also would change asylum laws in ways that immigration advocates say will limit the number of asylum seekers allowed into the country each year.
Last weekend, the president offered his biggest concession to Democrats yet, throwing in temporary extensions for DACA recipients and immigrants under Temporary Protected Status.
The Senate also rejected a Democratic spending bill, which has passed the House 231-180.
The Senate was unlikely to pass these bills since it would need 60 votes to do so, which neither side appeared to have.