WASHINGTON — Taking the same position as state officials have in other same-sex marriage cases, government officials in Ohio on Friday urged the Supreme Court to rule on the constitutionality of state laws against same-sex marriage.

“The country deserves a nationwide answer — one way or the other,” the state’s brief said. The state defended its ban even while asking the Court to review it.

The Ohio petition grows out of two cases in that state. Both focus on what is usually called the “recognition” issue: same-sex couples who already are married, and want the state to officially recognize their marriages.

One of the cases involves three couples who were married elsewhere and want the state to recognize both married parents on their children’s Ohio birth certificates, and a same-sex couple who were married in New York and are seeking the same thing for a child born in Ohio and adopted in New York.

The other case involves two men who were married in other states to their same-sex spouses, who later died; they are seeking to have their marriages acknowledged on the death certificates of their late spouses.

In taking the case to the Supreme Court, the couples raised the right-to-recognition question under the Fourteenth Amendment, as well as — for the New York couple — a claim that Ohio must recognize the New York adoption of an Ohio-born child under the Constitution’s Full Faith and Credit Clause.

In agreeing that the Supreme Court should agree to review the Ohio case, the state urged the Justices to rule only on the Fourteenth Amendment question. Because the Full Faith and Credit Clause issue, the state argued, raised a series of complicating issues, that question should not be addressed.

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With the Ohio response, there are now four new same-sex marriage cases that are nearly ready for the Justices’ first look. Only a Tennessee case, among the new cases recently filed, awaits a response from the state; that is due on Monday.

Two more cases are also on their way to the Court — from North and South Carolina.

If the Court’s staff sends some or all of the existing five cases to the Justices during the rest of this month, they all could be considered as soon as the Court’s January 9 Conference. Agreement by the Court to hear one or more of the cases at that time, or soon afterward, would be in time for a final ruling during the Court’s current Term, which will run to late June or early July.