A top congressional security official told senators on Tuesday that protection around lawmakers had increased since the assassination of a legislator in Minnesota, as members of both parties pressed for more funding to keep them safe on Capitol Hill and in their districts and states.

Tensions were high at the Capitol as lawmakers continued to grapple with the killing of one state lawmaker in Minnesota and her husband and the wounding of another and his wife. The shootings intensified questions simmering for years about how to protect members of Congress and their families amid increasing threats of political violence.

“The violence and threats against elected officials, including people in the Senate, has drastically increased,” Senator Chuck Schumer, Democrat of New York and the minority leader, said after a briefing by Jennifer A. Hemingway, the Senate sergeant-at-arms. “That means we need more protection. We need more money.”

Congress determines how much to spend on its own security as part of the annual appropriations process, though the president must sign funding bills.

Behind closed doors, Ms. Hemingway briefed senators on steps that had been taken to increase their security. And Mr. Schumer said senators in both parties pressed her about how to better protect members of Congress, including calling for more money to fund such safeguards.

In a statement, a spokesman for the Capitol Police said that officers had been working closely with federal, state and local law enforcement agencies to “enhance security for members of Congress” since the Minnesota shootings. The spokesman declined to discuss details of those efforts, citing security concerns.