By Brendan O'Brien

MILWAUKEE (Reuters) - Officials in Wisconsin's two largest counties on Monday reported brisk traffic from same-sex couples seeking marriage licenses after a federal judge's ruling last week that the state's ban on gay nuptials was unconstitutional.

The steady stream of couples seeking licenses in Milwaukee County and Dane County, which includes the state capital Madison, continued as the state attorney general awaited rulings from the federal judge and a U.S. appeals court on his request to halt marriages while the state appeals the decision.

The two counties issued 283 marriage licenses to same-sex couples, staying open late on Friday after the federal judge's ruling and for extended hours on Saturday before a possible stay like ones issued in cases from other states.

The office of Milwaukee County Clerk Joe Czarnezki said it had a small rush of marriage license applicants when doors opened Monday morning while officials in Dane County Clerk Scott McDonell's office said a line has formed for marriage licenses.

"It's more than steady already ... everyone is so happy, it's extremely exciting and upbeat," said Melanie Conklin, a spokeswoman for County Executive Joe Parisi.

Wisconsin Attorney General J.B. Van Hollen has asked U.S. District Court Judge Barbara Crabb to halt, at least temporarily, the issuance of marriage licenses to same-sex couples.

Crabb on Friday ruled that Wisconsin's ban on same-sex marriage was unconstitutional. She has scheduled a hearing on his request for Monday afternoon, according to court records.

Van Hollen on Monday appealed Crabb's ruling to the U.S. Court of Appeals for the Seventh Circuit, asking for an emergency stay to halt the marriages.

Crabb's ruling was the latest in a string of decisions by federal judges who have struck down gay marriage bans in a number of states.

Challenges to state bans gathered momentum last June when the U.S. Supreme Court struck down parts of the U.S. Defense of Marriage Act, ruling that legally married same-sex couples were eligible for federal benefits.

Not including Wisconsin, same-sex marriage is now legal in 19 states plus the District of Columbia, and the number of states could grow sharply if federal court rulings striking down bans in several states are upheld on appeal.

(Reporting by Brendan O'Brien; Editing by Doina Chiacu)