WASHINGTON — The Senate on Thursday passed a long-delayed disaster relief package, a step toward ending a monthslong impasse that had prevented the release of billions of dollars in aid for farmers and communities struggling to recover from an onslaught of natural disasters over the last two years.

Minutes after a tornado warning blared through the Capitol chambers, the Senate voted 85 to 8 to allocate $19.1 billion for recovery efforts across the country. While the package included $900 million for Puerto Rico that President Trump had objected to, it did not include funds for the southwestern border that the White House had pressed for.

“We took it all out. We’re going to try to push that separately when we come back,” Senator Richard C. Shelby, Republican of Alabama and the chairman of the Senate Appropriations Committee, told reporters, referring to the administration’s request for additional aid for the border. “It’s a good deal. This disaster issue has played on for months and months.”

Although most representatives have left Washington for a weeklong Memorial Day recess, House leaders hope to pass the emergency spending bill as soon as Friday using unanimous consent. But some House Republicans are likely to be discontent with the measure, and any lawmaker could block the motion and delay final passage until the full chamber returns.