North Dakota attorney general's office said it had not yet seen the suit and was not commenting. The 2004 voter-approved constitutional ban on same-sex marriage was passed by 73 percent of voters.
Legal experts said the lawsuit is largely symbolic, but could carry more serious weight.
"It's symbolic but sometimes symbolism is important, right? I think it has real, practical, actual effects on people nationwide and in North Dakota," said Carl Tobias, a professor at the University of Richmond School of Law who studies constitutional law.
Filed by Minneapolis attorney Josh Newville, who is also representing six South Dakota couples in a similar case, the lawsuit claims violations on three issues that are guaranteed in the 14th Amendment to the U.S. Constitution: equal protection, due process and right to travel.
Like the South Dakota lawsuit, the complaint seeks a declaration that the statute and constitutional bans are unconstitutional and asks that the state be prevented from enforcing the ban and be required to issue marriage licenses to same-sex couples and recognize gay marriages from other states. It also seeks reimbursement for lawyers and other costs.
"The state will incur little to no burden in allowing same-sex couples to marry and in recognizing the lawful marriages of same-sex couples from other jurisdictions on the same terms as different-sex couples," it states, while saying the couples are subject to "an irreparable denial of their constitutional rights."
Josh Boschee, who became the state's first openly gay legislator in 2012, said he believes North Dakota is much different place than it was 10 years ago and the lawsuit demonstrates that the issue is common throughout the nation.
"I think it shows that there's agreement in all 50 states that current law is unfair to lesbian and gay families," said Boschee.
In 19 states and the District of Columbia, gay couples already can wed, with Oregon and Pennsylvania becoming the latest to join the list when federal judges struck down their bans and officials decided not to appeal.
Before the lawsuit was filed, Tom Freier, executive director of the North Dakota Family Alliance, which campaigned to bring the measure to the North Dakota ballot in 2004, said any such challenge would face strong opposition.