Speaking in Prescott, Ariz., at a memorial for the firefighters who were killed June 30 while fighting the Yarnell Hill fire, Biden said the unit's motto -- "Duty, Integrity, Respect" -- "sums them better than anything I can think of."
"They saw their job not as a job but as a duty -- a duty -- to their fellow citizens," Biden said.
An estimated 6,000 people gathered for the memorial in an arena, while an estimated 2,000 watched on large TV screens in the parking lot outside, The Arizona Republic said. The crowd included firefighters from across the country, as well as former members of the Granite Mountain Hotshots.
Brendan McDonough, the only surviving member of the Granite Mountain Hotshots, read the "Hotshot Prayer" at the service.
"I am called to duty, Lord, to fight the roaring blaze. Please keep me safe and strong, I may be there for days.
"Be with my fellow crew members as we hike up to the top. Help us cut enough line for this blaze to stop.
"Let my skills and hands be firm and quick. Let me find those safety zones as we hit and lick.
"For if this day on the line I should answer death's call, Lord bless my hotshot crew my family on and all.
"Thank you and I miss my brothers."
Prescott Fire Department Division Chief Darrell Willis, wearing the uniform he had on the night the Granite Mountain Hotshots were killed, said at the service the unit "was the first and only hotshot crew in the nation and in my eyes they were the best out of the 108 hotshot crews in the nation."
Following the memorial, Biden, his wife, Jill, and several state and federal officials spent a few moments with members of each fallen firefighter's family, the Republic said.
The group included Rep. Kyrsten Sinema, D-Ariz.; U.S. Sen. John McCain, R-Ariz.; U.S. Sen. Jeff Flake, R-Ariz.; U.S. Secretary of Homeland Security Janet Napolitano -- a former governor of Arizona -- and U.S. Reps. Matt Salmon, Paul Gosar, Ann Kirkpatrick, Ron Barber and David Schweikert, all of Arizona.
"I just wanted to let folks know our hearts are with them," Sinema said. "We are privileged to be here. The service was tremendous.''
Each family received the International Association of Firefighters' gold medal of honor.
As the crowd left the arena, hundreds of firefighters lined both sides of the street leading out of the building.
The memorial came two days after a service Sunday in which 19 hearses brought home the bodies of the fallen firefighters at the end of a police motorcycle-led procession that covered about 125 miles from Phoenix, where autopsies were performed, to Prescott, the hometown of the Granite Mountain Hotshots.
Preliminary autopsies indicated the firefighters died of injuries such as burns and inhalation problems. A full autopsy report on each firefighter is expected to be completed and released within a couple of months.
During the weekend, firefighting officials said the Yarnell Hill fire had been largely reduced to hot spots after burning 8,400 acres. Operations section chief Carl Schwope said he expected full containment "sometime before July 12."
KPHO-TV, Phoenix, said at least 114 homes and other structures were lost to the lightning-sparked wildfire.
Texas principal bans speaking Spanish, stirs controversy
Caroline Berg Eriksen: Soccer player's wife triggers debate with post-birth selfie