Officials of Red Bank and Asbury Park either could not be reached or could not confirm that applications were being accepted.
Garden State Equality was one of the plaintiffs in the lawsuit that yielded the Sept. 27 decision by Superior Court Judge Mary C. Jacobson that the state's civil-union law violated same-sex couples' civil rights. She ordered that effective Monday, same-sex couples must be permitted to marry.
The Christie administration has appealed the decision and is seeking a stay of the order. Both actions are pending before the state Supreme Court.
Around the state, there has been considerable confusion - and little clarification - about whether the order means the processing of marriage-license applications should begin Monday or whether marriages could be held on that day. Under the state's 72-hour-wait requirement between applying for and getting a marriage license, new applications would have to be processed this week for marriages on Monday.
"Unless we hear otherwise from the New Jersey Supreme Court, this ruling is in effect," said Hayley Gorenberg, deputy legal director for Lambda Legal and one of the attorneys presenting the case. "We understand that mayors and other municipal officials are eager to open their doors and make it possible for same-sex couples to marry as soon as the law permits."
Shortly after 3 p.m. Thursday, an e-mail with some guidance was sent to municipal clerks by the state Bureau of Vital Statistics.
It said the office was "still awaiting legal direction on if and when we can start taking applications. At this point, you cannot take applications for same-sex marriages until you hear from this office that we have the authority to do so."
It also noted that amended forms were ready to go if there is not a stay.
Assembly Majority Leader Louis D. Greenwald (D., Camden) praised the municipalities that were reportedly forging ahead.
"I am thrilled to see local officials moving forward with efforts to establish marriage equality in their towns," Greenwald said in a statement. "Make no mistake, marriage equality will be the law of the land in New Jersey; it is a simple matter of when, not if."
Lambertville has not started processing applications, but the municipal clerk and registrar, Cindy Ege, said that if the Supreme Court did not issue a stay, she would start processing the applications Monday.
"If we are a go on Monday, I will be at the office at midnight," she said. "I have a lot of friends who are gay, and I will support them 100 percent."
Mayor David DelVecchio said he would be in his office then, too. He said he would be affirming the marriage of a couple who were already wed elsewhere and did not need to go through the waiting period.