New York (CNN) -- An organ played "New York, New York" as pallbearers -- from the New York City Police Department -- carried the simple wooden casket with a Star of David through hundreds of admirers, friends, family members and dignitaries, and out of the Temple Emanu-El in Manhattan on Monday to lay to rest the city's brash and outspoken three-term former mayor, Ed Koch, who died of congestive heart failure on Friday.
He was 88.
"I come today with the love and condolences of 8.4 million New Yorkers who really are grieving with you at this moment," said current New York City Mayor Michael Bloomberg as he delivered one of several eulogies for Koch beginning around 11 a.m.
"Although Ed -- on the other hand -- has got to be loving all this attention," Bloomberg joked.
"No mayor, I think, has ever embodied the spirit of New York City like he did. And I don't think anyone ever will. Tough and loud, brash and irreverent, full of humor and chutzpah -- he was our city's quintessential mayor," Bloomberg said. "He knew from the beginning that the key to success lay in throwing political caution to the wind.
"And it's easy to forget just how badly our city needed that kind of leadership -- because the New York that Ed inherited is almost unimaginable today: graffiti-filled subways, miles of abandoned buildings, filthy streets that were unsafe to walk in daylight, much less at night, a municipal government that was broke and had stopped functioning. ... Then came Koch," Bloomberg said.
"It is fair to say that the city we know today would not exist without him. Everything that David Dinkins and Rudy Giuliani and I accomplished has been built on the foundation that Ed laid."
Noting that Koch was to be buried at Trinity Cemetery in Upper Manhattan, Bloomberg added, "Just think about it: a Polish Jew in an Episcopal graveyard in a largely Dominican neighborhood. What could be more New York -- or even more Ed Koch?"
Former President Bill Clinton, who cut short a trip to Japan to attend, addressed the mourning crowd next. Holding a handful of letters of advice and opinion Koch had sent him when he was president, Clinton said no one had a better feel for "the impact of what government did on the real lives of people" than Koch.
The former president described how Koch advocated for tougher gun laws and said he would be proud of Gov. Andrew M. Cuomo for his recent effort to toughen New York state gun laws.
In his lifetime, Koch was known to look to his constituency and ask "How am I doing?"
On Monday, Clinton seemed to turn the question back on him, "Ed, we are all doing fine but we miss you and we miss you so much because we all know we are doing a lot better because you lived and served."
Koch's relatives spoke of him as a family man who always wanted to know what was going on in their lives.
A grandnephew, Noah Thaler, recounted a time Koch bragged to Clinton about the young man's accomplishments.
Diane Coffey, Koch's longtime chief of staff, said the key to Koch's gift for leadership was "an ability to meet people on their own terms without ever diluting his own distinctive personality."
Also at the services Monday were New York's U.S. senators, Charles Schumer and Kirsten Gillibrand; former mayors David Dinkins and Rudolph Giuliani; Gov. Cuomo; former governor Mario Cuomo; and other current and former city, state, federal and international government officials, including the Israeli consul general, Ido Aharoni.
"By the force of his own personality he led New Yorkers to believe that our best days weren't behind us, and he succeeded," Schumer told CNN.
Gillibrand described Koch as a great reformer and a friend from whom she'd ask advice on everything from Middle East policy to where to get the best Chinese food.
"He was mayor of this city during a time of crisis and he really brought the city together," she said.
"I think Ed Koch was himself. And too often nowadays people worry about how they look or what their image is or are they doing it right," said Christine Quinn, speaker of the New York City Council and rumored potential Democratic candidate for mayor in the city's 2013 election.
"Every time I asked him for advice," she said, he told her "to do what I thought was right, to have fun and if people didn't like it just 'bleep' 'em. And not a lot of elected officials live by those codes today. And if you do the right thing and you have some fun, you're doing the best you could possibly do. And that's a good thing."
An honor guard representing the city's police, fire, parks, sanitation and correction departments and the sheriff's office stood by the casket for the ceremony.
The service was officiated by David Posner, the synagogue's senior rabbi.
A private shiva will be held Tuesday at Gracie Mansion, the official residence of the city's mayor, on Tuesday, according to the ceremony program, and the family is requesting that contributions be made to the LaGuardia Community College Foundation.
Koch was a U.S. congressman from 1968 until he ran for New York City mayor in 1977. He served three terms as the city's 105th mayor, from January 1, 1978, to December 31, 1989.
CNN's Dana Ford and Steve Almasy contributed to this report.