Tom Brady, Julian Edelman and Rob Gronkowski parade through the city of Boston celebrating the Patriots' sixth Super Bowl title in 18 years. (0:56)

BOSTON -- An estimated 1.5 million jubilant fans jammed downtown Boston on Tuesday for a parade celebrating the New England Patriots' sixth Super Bowl title, clamoring for more with cheers of "We want seven!" and "Next year, right here!"

A party atmosphere enveloped the city as fans clad in team garb packed sidewalks in the mild weather and stood on tiptoe for a glimpse of quarterback Tom Brady, coach Bill Belichick and the rest of the team. Red, white and blue confetti rained down.

It's a familiar feeling in Boston. The parade came just four months after the city feted the Red Sox for their fourth World Series championship in 15 years.

"Getting to see Tom Brady again is always a special day, but the Patriots are amazing. Six-time champs," fan Lauren Mills said, adding that she still hasn't had her fill. Her message to Brady: "Go for No. 7. He still has how many fingers left? You know, four more rings to go."

Security was tight, and authorities said a dozen people -- including seven juveniles -- were arrested, and many charges were alcohol-related. One man who appeared intoxicated was taken away on a stretcher, and five of those arrested were involved in a brawl near the end of the parade route.

Mayor Marty Walsh warned fans not to throw anything. Errant beer cans slightly damaged the Red Sox World Series trophy last year.

Fresh from Sunday's 13-3 victory over the Los Angeles Rams in Super Bowl LIII in Atlanta, team members and their families took a two-mile swing through the city aboard Boston's iconic World War II-era amphibious "duck boats."

Brady held his pigtailed daughter, Vivian, and they waved and grinned at the crowd as players and team owner Robert Kraft took turns holding aloft the Lombardi Trophy. Belichick and his partner, Linda Holliday, beamed, and the storied coach doffed his cap.

Star tight end Rob Gronkowski, who has talked about retiring after this latest NFL title, whooped it up with his brothers and father. He and several other players removed their shirts and spent the second half of the parade cavorting bare-chested.

They waved large signs that read, "We Got Everything" -- a twist on the Patriots' motivational hashtag, "Everything We Got," that had become a theme this season.

At least one brave Rams fan, wearing one of the team's blue and yellow jerseys, hung out along the parade route.

Police estimated that about 1.5 million people attended, making it one of the largest crowds Boston has seen for a championship parade. Early trains and subways were jammed, overwhelming the area's transit system with what officials said was record ridership. The weather was unseasonably warm, with temperatures above 50 degrees and dazzling sunshine.

Unlike in past years, no post-parade rally with speeches was done. Officials didn't elaborate as to why.

Stephen Chhom, of Lynn, Massachusetts, was along the parade route overlooking the Statehouse with his friend Ricky Sok and Sok's six-year-old son, Raiyu.

"What made this year special were all the other fans doubting us," Chhom said, wearing a Julian Edelman jersey. "The record speaks for itself. Tom Brady and the rest of the team prove themselves every single time."

The Associated Press contributed to this report.