CONCORD, N.H. — Gay couples in New Hampshire can start applying for many of the rights and responsibilities of marriage as early as January under a law Governor Lynch signed yesterday establishing civil unions.

“We in New Hampshire have had a long and proud tradition taking the lead in opposing discrimination,” Mr. Lynch said. “Today that tradition continues.”

Couples who enter civil unions will have the same rights, responsibilities, and obligations as married couples. Same-sex unions from other states also would be recognized if they were legal in the state where they were performed.

Legislators who gathered for the bill signing packed the governor’s chambers and overflowed into an adjoining sitting room. They snapped photos and burst into applause as he signed it.

“I’ve listened, and I’ve heard all the arguments,” Mr. Lynch, a Democrat, said. “I do not believe that this bill threatens marriage. I believe that this is a matter of conscience and fairness.”

Episcopal Bishop V. Gene Robinson was among those attending. Although his consecration in 2003 as the first openly gay bishop in the Episcopal Church divided the worldwide Anglican Communion to which it belongs, Bishop Robinson and his longtime partner plan to take advantage of civil unions.

“This is not a radical departure,” Bishop Robinson said of the bill. “This is a real confirmation of what New Hampshire has always been about: the freedom of its own citizens and fairness for everyone.”

Bishop Robinson said he will not direct Episcopal priests in the state to bless same-sex unions, letting priests decide that individually. Such blessings have been another divisive issue for Episcopalians and the Anglican union.

Massachusetts alone among the states allows gay marriage. Connecticut, Vermont, New Jersey, Maine, California, and Washington allow either civil unions or domestic partnerships, and Oregon will join the list with New Hampshire in January. Hawaii extends certain spousal rights to same-sex couples and cohabiting heterosexual pairs.