Friends, allies and former rivals of Joseph I. Lieberman, who died on Wednesday, offered condolences and praise for the four-term senator from Connecticut who was once a standard-bearer of the Democratic Party.

Mr. Lieberman, who was Al Gore’s running mate in the 2000 presidential election, had made his presence felt in politics long after his defeat in that race. He was the deciding Senate vote that led to the passage of the Affordable Care Act, allowing him to veto specific provisions like a public health insurance option.

He had also more recently aided the centrist organization No Labels in its search for a 2024 presidential candidate.

“Senator Lieberman leaves behind a void that cannot be filled,” the group said in a statement. “But we are honored to have known him, and we hope his family can find comfort in the difficult days ahead knowing the tremendous impact that he had.”

Mr. Gore, the former vice president who chose Mr. Lieberman as his running mate during the 2000 election, said it had been “an honor to stand side-by-side with him on the campaign trail.”

He added, “I’ll remain forever grateful for his tireless efforts to build a better future for America.”

Mr. Gore continued: “He was a truly gifted leader, whose affable personality and strong will made him a force to be reckoned with. That’s why it came as no surprise to any of us who knew him when he’d start singing his favorite song: Frank Sinatra’s ‘My Way.’ And doing things Joe’s way meant always putting his country and the values of equality and fairness first.”

Former President George W. Bush, the victor — with Dick Cheney — over the Gore-Lieberman ticket in 2000, said: “In both loss and victory, Joe Lieberman was always a gentleman. I’m grateful for Joe’s principled service to our country and for the dignity and patriotism he brought to public life.”

Mr. Bush added, “Joe was as fine an American as they come and one of the most decent people I met during my time in Washington.”

Senator Lindsey Graham of South Carolina, who had struck a close friendship with Mr. Lieberman and Senator John McCain of Arizona — the men referred to themselves as “the three amigos” — said the news of Mr. Lieberman’s death was “devastatingly sad.”

“The good news, he is in the hands of the loving God,” Mr. Graham said. “The bad news, John McCain is giving him an earful about how screwed up things are.” Mr. Graham signed his statement as “the Last Amigo.”

Mr. Lieberman cast the 60th and deciding vote under Senate rules to pass the Affordable Care Act in 2010, a signature achievement of President Barack Obama’s administration. “Joe Lieberman and I didn’t always see eye-to-eye,” Mr. Obama said in a statement, “but he had an extraordinary career in public service, including four decades spent fighting for the people of Connecticut.”

Former Gov. Chris Christie of New Jersey, who had spoken to Mr. Lieberman as he considered running for president on the No Labels ticket, offered his condolences hours after publicly turning down the group’s offer. Mr. Lieberman was the centrist organization’s founding chairman and had recently served as its co-chairman.

“I am sad to lose him as a friend and as an example for how to conduct yourself in public life,” Mr. Christie said, adding that “the country is greater for his example and lesser today without his fearless leadership.”