“I don’t think this is the time to hesitate and wrangle over how to pay for something as acute to public health as this is,” said Representative Greg Walden, Republican of Oregon.

The quick action was a recognition of the urgent need described by government health officials to respond to the virus, and mounting dissatisfaction among lawmakers in both parties with the funding request submitted by the Trump administration. The Senate is also expected to approve the funding, sending the measure to the White House, where President Trump said at a news conference last week that he would “spend whatever is appropriate” to counter the outbreak.

“This should not be about politics,” Senator Richard C. Shelby, Republican of Alabama and chairman of the Senate Appropriations Committee, said in a statement. “This is about doing our job to protect the American people from a potential pandemic. We worked together to craft an aggressive and comprehensive response that provides the resources the experts say they need to combat this crisis.”

Top appropriators struck a deal to provide $7.8 billion in new money, rebuffing the administration’s request to use more than $1 billion in existing funds shifted from within health agencies. Under the bill, the funds could be used only to combat the spread of the coronavirus and other infectious diseases.

The measure would also reimburse $136 million that the administration had previously transferred from other programs in the Department of Health and Human Services. Ahead of Congress approving the emergency funds, the agency said it would transfer $25 million of those funds to states and cities that have already spent substantial resources on the response to the virus. The money would go toward lab equipment, staffing, shipping and infection control, among other things.