HARTFORD, Conn. — An attorney for eight gay couples told the state Supreme Court yesterday that their constitutional rights have been violated by the state’s refusal to grant them marriage licenses.

Connecticut was the first state to allow civil unions without court pressure, but the couples say that’s not enough.

They want the court to rule that the state’s marriage law is unconstitutional because it applies only to heterosexual couples, effectively denying gay couples the financial, social, and emotional benefits of marriage.

“What is denied to these families is something that goes to the heart of equal protection, which is the right to be part of the fabric of society when they are just the same as other couples and other families,” said their attorney, Bennett Klein.

Assistant Attorney General Jane Rosenberg, representing the state, argued that civil unions give gay couples the same rights by state law as married couples.

The question “is really, is the Legislature constitutionally required to use the word marriage when it’s referring to the package of rights and benefits it has given to same-sex couples. And the answer is clearly no,” Ms. Rosenberg said.

Arguments wrapped up after about three hours yesterday, and the justices are expected to rule later this year. Attorneys on both sides say a decision in the couples’ favor could have nationwide implications for states that have adopted or are considering civil union-like legislation.

Currently, only Massachusetts allows same-sex couples to marry. Connecticut, Vermont, California, New Jersey, Maine, and Washington have laws allowing either civil unions or domestic partnerships, with New Hampshire set to join in January. Hawaii extends certain spousal rights to same-sex couples and cohabiting heterosexual pairs.

The Connecticut couples who sued have been together between 10 and 32 years and say civil unions are inferior to marriage and violate their rights to equal protection and due process.

Married couples have federal rights related to taxes, Social Security beneficiary rules, veterans’ benefits, and other laws that people in civil unions don’t have. Because civil unions aren’t recognized nationwide, other rights, such as the ability to make medical decisions for an incapacitated partner, disappear when couples cross state lines.

The couples’ claim was dismissed last year by a judge who said they received the equality they sought when Connecticut passed its civil unions law. The couples appealed.

In court yesterday, Mr. Klein replied that the fundamental principles of marriage are not based on gender. “It is really a relationship of two legal equals based on mutual consent by which they take responsibility for each other, and that relationship is protected by the state,” he said.

The suit names the state Department of Public Health and the Madison town clerk’s office, which denied licenses to the couples based on state Attorney General Richard Blumenthal’s advice.