New York (CNN) -- A city official married the first couple in New York City to wed under the state's new law allowing same-sex marriage Sunday.

Phyllis Siegal, 76, and Connie Kopelov, 84, were married in a chapel at the city clerk's office as a crowd of onlookers cheered.

The two, of New York, have been together for 23 years. Kopelov left the clerk's office in a wheelchair, but used a walker to approach reporters.

"Your cheers are wonderful," Siegal told well-wishers outside the office.

She told reporters the experience was "just so amazing. It's the only way I can describe it."

Hundreds of same-sex couples heard the news Friday that they made the cut in the marriage lottery that New York state instituted for Sunday, the day that the state's Marriage Equality Act took effect.

"These are two independent people who are joining together because they can see and they can feel how much better their lives will be," city clerk Michael McSweeney said as he married Siegal and Kopelov. "We are grateful that they are allowing us to share this truly momentous ceremony with them."

The New York City clerk's office has been flooded with more than 2,600 requests for marriage licenses since the wording on the online application was changed from "Groom and Bride" to "Spouse A and Spouse B."

The office could handle less than a third of those requests -- gay or straight -- on Sunday, according to a press statement the city released earlier in the week. The lottery was set up to allocate 764 slots for couples who want to obtain marriage licenses and/or be married at city clerk's offices on Sunday.

Buffalo residents Kitty Lambert and Cheryle Rudd claim to be the first couple married in the state. The two exchanged vows at 12:01 a.m. Sunday in Niagara Falls, according to CNN affiliate WGRZ.

Couples began lining up outside the clerk's office in New York City before the ceremonies began Sunday. Some women wore wedding gowns, while some men wore suits or tuxedos.

If all 764 weddings actually take place on Sunday, it will set a one-day record for the city.

"Marriage equality is alive and well in every borough of New York City right now," said Christine Quinn, speaker of the New York City Council, who is also gay. She said watching the weddings "sent a chill up my spine."

Marcos Chaljub and Freddy Zambrano were married after Siegal and Kopelov. The two tearfully said their vows as friends hovered and snapped pictures. "You're married!" one declared as celebratory hugs were exchanged afterward.

Chaljub and Zambrano conducted last-minute preparations Saturday for their wedding, picking up bouquets of wildflowers for their bridesmaids and champagne for a family brunch afterward. The couple has been together for five years.

"I have certain people in my life, they're not totally OK with it, but they accept it, and just the fact they respect us because of that, it's really the most that I can ask for," Chaljub told CNN's Susan Candiotti.

The two have been wearing rings for five years, and said they don't plan to exchange new ones. "We're just going to polish them up and exchange them again," Chaljub said.

As with many weddings, there were some comical moments.

Chaljub momentarily forgot which finger to put Zambrano's ring on. "Is it this one?" he asked.

Asked whether he took Michael Elasser, 56, as his spouse, 60-year-old Douglas Robinson responded, "You bet your life I do!" The couple's two adopted sons, ages 25 and 22, attended the ceremony.

"This is one of the great things about America, this diversity," Robinson said. "I'm so proud to be an American today, but I'm particularly proud to be a New Yorker."

New York Rabbi Sharon Kleinbaum of Beit Simchat Torah congregation, who has lobbied for legalizing same-sex marriage, set up a station for couples desiring a religious ceremony after the civil one.

New York legalized same-sex marriage in June. The Marriage Equality Act was a priority for Gov. Andrew Cuomo after winning election in November. The law was passed under a Republican-led Senate after days of delays and negotiations between the two parties.

Quinn announced that a drawing will take place Monday to award a honeymoon package to one newly-married couple in each borough. The package will include two nights in a Manhattan hotel; dinners; tickets to a museum, the Empire State Buidling, a Broadway show and Cirque du Soleil; and Macy's gift certificates.

However, opponents of the new law were planning to gather Sunday afternoon at rallies organized by the National Organization for Marriage in New York, Albany, Rochester and Buffalo. A handful of protesters were outside the city clerk's office in Manhattan Sunday morning.

Quinn told CNN that New York is the place where the LGBT (lesbian, gay, bisexual, transgender) movement was born, and a place the world looks to.

"All eyes are upon it, and I believe it is going to help propel this movement forward faster than any of the other states have," Quinn said.

Massachusetts, Connecticut, Iowa, Vermont and New Hampshire also allow same-sex marriage, as does the District of Columbia.

CNN's Jesse Solomon and Steve Kastenbaum contributed to this report.