In a motion filed in the New Jersey Supreme Court, the couples argue that even though New Jersey offers civil unions to gay couples as the state's response to the 2006 order, the government, hospitals, schools, employers and other institutions do not always recognize their full rights.
Seven couples filed the original lawsuit seeking equal treatment. Six couples plus the surviving partner of the seventh are parties to the motion filed Thursday, said Hayley Gorenberg of Lambda Legal, a lawyer representing the group.
"We came back to the court to turn equal rights on paper into equal rights in the real world," Gorenberg said.
Among possible court action, the court could agree with the group or reject the motion, agree but require legislative action to legalize gay marriage, or appoint a special master to study the issue.
For most of the past decade, New Jersey has been one of the states at the vanguard of the battle over expanding recognition of gay relationships. It's one of a handful of states where social conservatives have not been able to amend the state constitution to ban gay marriage.
In 2006, the state Supreme Court ruled unanimously that gay couples deserved equal treatment. But the court ruled by a 4-3 vote that the state did not have to recognize them as married. Instead, the court left details of their legal status up to the Legislature, which responded by making the state the third to offer civil unions.
New Jersey is now the only state with civil unions. Gay marriage is legal in Connecticut, Iowa, Massachusetts, New Hampshire, Vermont, and Washington, D.C.
The unions offer the name but not the title of marriage. Through February, 4,487 couples had registered.
Gay rights groups tried to get lawmakers to reconsider and recognize gay marriage, but the bill died after the state Senate voted it down in January. Supporters say they had the momentum until November, when Republican Chris Christie, who opposes gay marriage, was elected governor.
Advocates point to several changes since the court's ruling. First, they say, civil unions have not done what they intended to do.
The state's Civil Union Review Commission - a group opponents say was biased in favor of expanding gay rights - found as much in a report in 2008.
Couples have reported hardships such as not being able to see their partners in the hospital, being denied health insurance for their partners and having problems in town halls getting the forms for civil union licenses.
Mark Lewis, one of the seven couples, said that when he and partner Dennis Winslow entered into a civil union, it didn't feel like they were married. He said that's because it seemed like a bureaucratic formality.
"Nobody ever congratulated us," he said. "We didn't get any civil union presents. No one congratulated us when we updated our wills, either."
Many say the different treatment comes largely because the law is hard to understand.
Len Deo, president of the New Jersey Family Policy Council, one of the state's leading opponents of gay marriage, said that civil unions are working well. He said the state Civil Rights Commission has received only a dozen complaints about the practice in more than three years and all have been rectified.
"They started off in the courts. The courts gave a remedy. The remedy went to the legislature. Garden State Equality has done nothing since the enactment of the civil union law but try to discredit it," Deo said, referring to the state's main gay rights political group.
But at a state Senate committee hearing in December, several opponents of gay marriage said civil unions were not working. They said the right course is to change the law so they work better rather than allow gay marriage.