Tom Udall makes the case for killing the filibuster to fix a broken Senate.

Calling the Senate a “graveyard for progress,” Senator Tom Udall, Democrat of New Mexico, used his farewell address on Tuesday to urge his colleagues to fix a broken institution by gutting the legislative filibuster and changing a culture that he said values partisanship over the country’s best interests.

“I’m not the first to say this in a farewell address, and I won’t be the last, but the Senate is broken,” said Mr. Udall, who is retiring after 12 years. “The Senate is broken,” he repeated for emphasis.

A former attorney general and a member of a storied political family from the West, Mr. Udall has been trying to reform the filibuster almost since he arrived in the Senate in 2009 after five terms in the House. In an interview with The New York Times last week, he laid out why he saw the 60-vote threshold to advancing bills as an impediment to coming up with answers for the existential problems of the moment, such as climate change.

“The filibuster came to be through historical accident,” he said on the Senate floor on Tuesday. “The reality of the filibuster is paralysis — a deep paralysis.”

Mr. Udall also lamented the state of American politics, calling the country’s campaign finance system “out of control.”

“Secret money floods campaigns to buy influence, instead of letting the voters speak,” he said. “Voting rights are under attack. We can do our best to be good people in a system like that, but it’s no surprise that America’s faith in government is declining. These structures are antidemocratic. They reward extremism. They punish compromise.”

Mr. Udall is the second senator in as many weeks to use his farewell speech to lament the current state of the chamber under the leadership of Senator Mitch McConnell, Republican of Kentucky. Mr. McConnell’s friend, Senator Lamar Alexander, Republican of Tennessee, who is retiring after 18 years, described the Senate last week as “like joining the Grand Ole Opry and not being able to sing,” concluding, “It’s a real waste of talent.”

But Mr. Alexander — who is a former governor, cabinet secretary, presidential candidate and university president — concluded that senators would be making a fatal mistake if they eliminated the filibuster.

“It would basically destroy the Senate,” Mr. Alexander said. Instead, he argued that senators should rediscover the lost art of allowing debate on a variety of legislative changes rather than blocking them outright, to allow the chamber to return to a more bipartisan process.