A federal lawsuit has been filed against the US state of Ohio challenging its constitutional ban on equal marriage.

Two men from the state filed the lawsuit on Friday in Cincinnati against the state’s Governor, Attorney General and the Cincinnati health department registrar, who is responsible for filing death certificates.

James Obergefell and John Arthur filed the lawsuit as Mr Arthur is terminally ill, and with a view to having his death certificate to show that the couple are married.

The couple married in Maryland, a US state which allows same-sex marriages. Mr Arthur has amyotrophic lateral sclerosis.

The lawsuit aims to have the court rule that Ohio’s law and constitution violate their rights, including equal protection.

Governor John Kasich’s spokesman told the Columbus Dispatch that he believes that marriage is between one man and one woman. He declined to comment further.

A second high-profile Republican in the US state of Ohio, Jim Petro, the former attorney general, last week came out in support of equal marriage.

Equal marriage advocacy group FreedomOhio hopes to put a constitutional amendment on the ballot for Ohio later this year or next, which would remove the 2004 amendment which banned equal marriage.

In 2004, the amendment banning equal marriage passed with 62% of voters supporting.

Petro was the second Ohio Republican to announce his support, as Senator Rob Portman who was among the original sponsors of the Defense of Marriage Act (DOMA) became the first to announce that he had changed his anti-equal marriage stance. It followed the personal revelation of his own son’s coming out as gay.

The pair’s support for same-sex marriage could prove to be influential as FreedomOhio intends to put the issue before votes in the 2014 general election. To get on the ballot the organisation must find 385,245 signatures.

Following shortly after Portman’s announcement was GOP Senator Mark Kirk, who also came out in support.

Writing in an op-ed shortly after Kirk’s revelation was, Republican Senator Lisa Murkowski of Alaska, who announced her support for measures towards marriage equality, and became the third Republican Senator to do so.