By Rebecca BallhausKristina Peterson and Gordon Lubold, Wall Street Journal–

President Trump said Friday he had reached a deal with congressional leaders to reopen the government for three weeks while negotiations over border security funding continue, marking at least a temporary concession by the president to Democrats.

Speaking in the Rose Garden, Mr. Trump said he would sign a bill to open the government until Feb. 15 and start negotiations between the House and Senate over a full-year bill funding the Homeland Security Department, which oversees the border.

“After 36 days of spirited debate and dialogue, I have seen and heard from enough Democrats and Republicans that they are willing to put partisanship aside, I think,” Mr. Trump said.

The stopgap spending bill will provide no immediate funding for a border wall. Mr. Trump said he would continue to push for funding for such a barrier in the next three weeks, declaring: “Walls shouldn’t be controversial.”

He thanked federal workers for going more than a month without pay and said he would ensure they received back pay “very quickly or as soon as possible.”

The shutdown began Dec. 22 over a clash between the president and Democrats over whether to fund a border wall, which Mr. Trump says is key to national security and Democrats say is unnecessary. The president had considered declaring a national emergency to try to divert funds from elsewhere in the government to fund a wall, which he described Friday as a “powerful alternative” that he didn’t want to use.

If a stopgap spending bill is passed and signed on Friday, it will reopen the government on the 35th day of the impasse.

On Friday, federal workers missed their second full paychecks. The Federal Aviation Administration also ordered delays at New York’s LaGuardia Airport and other major airports, citing staffing shortages—the first sign the shutdown is interfering with the nation’s air travel.

For weeks, Democrats have urged the president to reopen the government while negotiations continue. Republican senators have been talking with increasing urgency in recent days about passing a stopgap spending bill.

The stopgap spending bill would include an extension of border security funding at current levels, which includes $1.3 billion for border security but not expressly for a wall.

The Senate could vote on the measure later Friday, with lawmakers expected to be in town. House lawmakers aren’t likely to be in Washington, but if Republicans agree, the chamber could pass it with a voice vote even if most lawmakers are gone.

The tentative agreement comes one day after rival proposals to end the shutdown failed in the Senate. After those bills failed—one of which Mr. Trump had proposed last weekend—Mr. Trump said he would be willing to support a short-term deal reopening government if it included a down payment for a border wall or barrier, and that he would accept a “reasonable” agreement between Senate Majority Leader Mitch McConnell (R., Ky.) and Mr. Schumer as long as it contained wall funding.

The two votes Thursday afternoon were the first the Senate had taken to reopen the government since the shutdown began on Dec. 22.

Write to Rebecca Ballhaus at Rebecca.Ballhaus@wsj.com, Kristina Peterson at kristina.peterson@wsj.com and Gordon Lubold at Gordon.Lubold@wsj.com