WASHINGTON — Gay and lesbian couples filed petitions on Friday asking the Supreme Court to decide whether there is a constitutional right to same-sex marriage. The petitions arrived eight days after the United States Court of Appeals for the Sixth Circuit, in Cincinnati, upheld bans on same-sex marriage in Kentucky, Michigan, Ohio and Tennessee.

The fast pace of the filings was an effort to ensure that the justices be able to hear and decide a case before the current Supreme Court term ends in late June.

On Oct. 6, the Supreme Court surprised most observers by turning down petitions seeking to appeal rulings striking down same-sex marriage bans in Indiana, Oklahoma, Utah, Virginia and Wisconsin. When the Supreme Court acted, there was as yet no disagreement among the federal appeals courts, a criterion the justices often consider in deciding whether to agree to hear a case.