WASHINGTON — President Biden paid tribute on Sunday to former Vice President Walter F. Mondale, hailing “one of the great giants of American history” who inspired him and many other Americans to believe in public service even in dark times.

Mr. Biden flew to Minneapolis for a memorial service that had been postponed for a year because of the coronavirus pandemic to honor Mr. Mondale, a friend of five decades and colleague from their days in the Senate who died in his sleep in April 2021 at age 93.

“It’s up to each of us to reflect that light that Fritz was all about, to reflect Fritz’s goodness and grace, the way he made people feel, no matter who you were,” said Mr. Biden, using the former vice president’s nickname. “Just imagine what our nation could achieve if we followed Fritz’s example of honor, decency, integrity, literally just a service for the common good. There would be nothing — nothing, nothing, nothing — beyond our reach.”

It was Mr. Biden’s second memorial service in just five days, following one last week for former Secretary of State Madeleine K. Albright at Washington National Cathedral. But Mr. Mondale had no desire to have his body lie in state or to be remembered in a grand celebration in the nation’s capital, preferring a simpler, more characteristically humble memorial in his home state of Minnesota.

There was, indeed, a quintessentially “Minnesota nice” quality to the event. Eulogists spoke of Mr. Mondale’s Norwegian stoicism, Midwestern values and dedication to helping others. The marching band from his cherished University of Minnesota played the “Battle Hymn of the Republic.” Lillian Hochman, a young Minnesota actress, sang “Tomorrow” from the musical “Annie,” a Mondale favorite.

Mr. Mondale was among the Democratic senators who encouraged Mr. Biden to take his seat after winning the 1972 election even though the candidate’s wife and daughter had just died in a tragic auto accident. The two went on to serve together in the Senate for four years and for another four years when Mr. Mondale was vice president under Jimmy Carter. Mr. Mondale and Mr. Biden were both exemplars of a different generation of Washington Democrats that has now mostly passed from the scene.

While serving under Mr. Carter from 1977 to 1981, Mr. Mondale set a standard for the vice presidency that later benefited Mr. Biden. Rather than just an ornamental figure whose main job was checking on the health of the president each morning, as most of his predecessors had been, Mr. Mondale set out to make the vice president a central figure in Mr. Carter’s administration.

He negotiated to be the first vice president to have an office in the West Wing, just down the hall and around the corner from the Oval Office, and he insisted on having a voice in most of the major issues of the day. His memo to Mr. Carter outlining his expansive view of the job later became a template for most if not all of the vice presidents who followed — including Mr. Biden, who consulted it when he assumed the office under President Barack Obama.

Mr. Mondale also paved the way for the current holder of his old job. During his 1984 campaign for president, he selected Representative Geraldine Ferraro of New York as his running mate, making her the first woman to run on a major-party ticket for vice president, although their bid fell short. Thirty-six years later, Vice President Kamala Harris broke that glass ceiling as part of Mr. Biden’s ticket.

But Mr. Mondale’s campaign in 1984 marked a low point for Democrats as he lost 49 states to Ronald Reagan, capturing only Minnesota and the District of Columbia. Despondent Democrats, including Mr. Biden, who ran for president unsuccessfully four years later, saw the campaign as a model for what not to do, most notably Mr. Mondale’s frank admission that he would raise taxes. Mr. Mondale nonetheless took his defeat with dignity and later went on to serve as ambassador to Japan under President Bill Clinton.

Senator Amy Klobuchar, a Minnesota Democrat and self-described “Mondale geek,” noted that Mr. Mondale set an example not just in victory but in defeat.

“None of it was easy,” she said. “But when saddled with enormous setbacks, Fritz didn’t stand down, he stood up. He didn’t crawl under his desk or hide from public view, he simply found a different way to serve.”

Jon Meacham, the presidential historian who delivered the keynote eulogy on Sunday, said that there were safer cars, cleaner rivers, children who would not go hungry, and women and Black Americans who would have greater opportunities because of Mr. Mondale.

“He never stopped believing in this country,” Mr. Meacham said. “He never stopped fighting for its people. Thankfully, he never stopped defending democracy. He never stopped and nor, in his memory, must we.”