Senator Mitch McConnell, the majority leader, announced on Thursday that President Trump planned to declare a national emergency so he can bypass Congress and build his long-promised wall along the southwestern border.

That raised the prospect of a constitutional clash with lawmakers over who controls the federal purse.

Mr. McConnell said the president would take action after signing a bill to keep the government open but not fund his wall.

"Sure, yeah," McConnell told reporters Thursday morning when asked if he has the votes to pass the legislation later in the day.

Asked if he’s received definitive assurances from the White House, McConnell said: “They’re reviewing it, as they should. . . . I’m hopeful he’ll sign it.”

The Senate is aiming to vote on the 1,159-page bill Thursday afternoon, and the House is expected to follow Thursday evening. The legislation would fund nine Cabinet departments and dozens of other agencies through Sept. 30, removing — for now — the threat of another government shutdown and political brinkmanship over Trump’s demands to fund a U.S.-Mexico border wall.

The compromise provides $1.375 billion for 55 miles of new fences along the border in Texas, far short of the $5.7 billion Trump had sought for 234 miles of steel walls. The final number for border barriers is also less than deals that were on the table last year before Trump pushed the government into a record-long 35-day shutdown in an unsuccessful attempt to get all the wall money he wants.

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In an unusual incident as the Senate came into session Thursday morning, Sen. Charles E. Grassley (R-Iowa) — who was presiding — amended the chaplain’s opening prayer to offer his own plea.

“Let’s all pray that the president will have wisdom to sign the bill so government doesn’t shut down,” Grassley said from the chair, a rare breach of Senate decorum that reflected the depth of lawmakers’ angst over the events of recent months.

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“The agreement is a reasonable compromise. It provides additional funding for smart, effective border security. It does not fund the president’s wall, but it does fund smart border security initiatives that both parties have always supported,” Senate Minority Leader Charles E. Schumer (D-N.Y.) said on the Senate floor. “Most importantly, it will keep our government open.”