New Jersey enacted civil unions in late 2006.
Assemblyman Gary Schaer (D., Passaic) said that as an Orthodox Jew, he could not vote yes.
"This is not something which my religion allows," he said, adding that his vote would not change if Christie vetoed the bill and the Assembly tried to override it.
In the Senate, two Republicans had voted in favor of the same-sex marriage bill, including Sen. Diane Allen of Burlington County.
Four members were absent for the Assembly vote, one Democrat and three Republicans.
Before the Assembly took up the bill, it honored a number of civil-rights heroes, including Thomas Mayfield of Willingboro, one of the original Tuskegee Airmen who fought during World War II.
The presentations dovetailed with Democrats' argument that denying marriage to same-sex couples deprives them of their civil rights. Civil unions, they argued, are an attempt to keep gays "separate but equal," an experiment that has failed. Same-sex couples sometimes struggle for recognition in medical situations or with their employers.
Assemblywoman Pamela Lampitt (D., Camden) said a lesbian couple she knows was denied a mortgage because the women were forced to file for it separately.
"They could not say, 'We're married,' " she said.
Assembly Speaker Sheila Oliver (D., Essex), the first African American woman to lead the chamber, said barring same-sex couples from marriage was no different from laws that once forbade members of different races to marry. Gay couples are fighting against "one of the last legalized barriers to equal rights," she said.
But Assemblywoman Nancy Munoz (R., Essex) said civil unions were working. She wants voters to decide in a referendum whether they approve of gay marriage.
"I trust the people of New Jersey and I believe that they should be allowed to voice their opinion through a vote," she said.
Democrats argue that a minority group's rights should not to subjected to the "whims of the majority."
Assembly Majority Leader Louis Greenwald (D., Camden) said he understood that many members had "nervous feelings" about voting on the bill.
"Welcome to the oath that you have taken," he said.
Freshman Assemblyman Benjie E. Wimberly (D., Passaic) said he lived in a district where hundreds of churches called him, urging him to vote no on gay marriage.
"I feel compelled as a man with ancestry that comes from slavery . . . to fight for what is right regardless of what individuals may think," he said of his vote in favor. "I'll ride back home to the 35th District, regardless of what the popularity of this is, knowing in my heart that I've done the right thing."
Hundreds of supporters and opponents arrived at the Statehouse early Thursday. Some opponents arrived with church groups on buses and wore red.
"I respect their decision, but this is a problem for the children," said Julio Maotta, 52, of Elizabeth, who traveled to Trenton with about 50 others from his El Shaddai Church in Roselle. He said he did not want children to learn in school that homosexuality is acceptable.
Charles Paragian, 49, of Little Ferry, said he attended because he, too, worried about his children: He wants all six of them to treat people equally, regardless of their sexual orientation.
He and his partner of 21 years have adopted three boys and three girls who were in foster care.
"We have to start thinking about the children. New Jersey allows us to adopt children but we're not legally allowed to protect them," he said.
Paragian said he and his partner had not filed for a civil union because it was not the equivalent of marriage.
Senate President Stephen Sweeney (D., Gloucester) has said he was confident he could find the three additional votes needed in his chamber to override a gubernatorial veto.
But in the Assembly, where Democrats hold a 47-32 advantage with one vacancy, 54 votes would be needed to override a veto.
Sweeney has led the effort to resurrect the issue. He has said he regrets abstaining two years ago, when same-sex marriage failed in the Senate, 20-14. At the time, Gov. Jon S. Corzine, a Democrat, had said he would sign the bill if it got to his desk.
Six states and the District of Columbia recognize gay marriages. Washington state's new gay marriage law is scheduled to take effect in June.
However, 30 states have adopted constitutional amendments aimed at preventing gay marriage, most by defining marriage as a union between man and woman.
By law, the Assembly has until the end of the day Friday to give the bill to Christie.
Earlier, the Assembly swore in Betty Lou DeCroce to take the seat of her late husband, former Minority Leader Alex DeCroce, who died in the Statehouse Jan. 9 after a marathon session of voting on the final day of the 2010-11 legislative session. He was 75.
Contact staff writer Joelle Farrell at 856-779-3237, email@example.com, or @joellefarrell on Twitter.