DENVER — A federal appeals court cleared the way on Tuesday for same-sex marriages to continue across Utah, denying an emergency request from state officials to halt a flood of unions that began after a lower-court judge declared the state’s ban on same-sex marriage to be unconstitutional.

Advocates of same-sex marriage cheered the ruling from the United States Court of Appeals for the 10th Circuit, in Denver, while the Utah attorney general’s office said it would ask the United States Supreme Court to temporarily halt same-sex marriages in the state until the legal battles could be resolved.

On Friday, Judge Robert J. Shelby of Federal District Court sent shockwaves through the conservative state and touched off jubilant impromptu weddings by declaring that Utah’s 2004 voter-approved ban on same-sex marriage violated the United States Constitution and denied same-sex couples their “fundamental right” to marriage.

Even as Republican leaders in Utah condemned the ruling as an activist judge’s usurpation of the voters’ will and vowed to appeal, gay couples across the state poured into government offices to marry. About 700 couples have received marriage licenses since Friday, according to a tally by The Deseret News, from the more liberal capital of Salt Lake City to conservative towns in southern Utah.