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.”