The State Department’s focus on biological parentage means that if the source of the sperm and egg do not match married parents, the case can be treated as “out of wedlock,” a designation that comes with a higher bar to transmit citizenship.

Mr. Gregg, who moved to the United States to be with his husband, did not meet a five-year residency requirement. His lawyers say that requirement would not have applied if they had been treated as the married couple they are.

For two married United States citizens, “all the law requires is that one of them lived in America for at least one day,” said Aaron Morris, the executive director of Immigration Equality, which has worked on all three lawsuits.

“Marriage is so fundamental to how you define a family,” he said. “To disenfranchise a little girl of citizenship because she has two dads is invidious discrimination that has been struck down time and time again.”

The State Department declined to comment on Tuesday, citing pending litigation. In court documents, the department has argued that the policy does not discriminate and applies to opposite-sex and same-sex couples alike.

But gay couples argue that they are far more likely to be questioned about their conception methods when applying for citizenship. Immigration Equality said that it had heard from at least three dozen families in similar situations since mid-2017; by the organization’s account, most were same-sex couples.

In court documents, the State Department has said that rules for passing down citizenship for children born abroad are important for preventing fraud and ensuring that children born abroad have a sufficient connection to the United States to warrant citizenship.