BIRMINGHAM, Ala. — Amid conflicting signals from federal courts and the chief justice of Alabama’s Supreme Court, some Alabama counties began granting marriage licenses to same-sex couples Monday in a legal showdown with echoes of the battles over desegregation in the 1960s.

In major county seats like Birmingham, Montgomery, and Huntsville, same-sex couples lined up outside courthouses as they opened and emerged smiling after being wed.

At the Jefferson County Courthouse here, Judge Michael G. Graffeo of Circuit Court officiated at the civil wedding of Dinah McCaryer and Olanda Smith, the first to emerge from the crowd of same-sex couples on Monday morning.

“I now pronounce Olanda and Dinah are married spouses, entitled to all rights and privileges, as well as all responsibilities, afforded and placed upon them by the state of Alabama,” Graffeo said.

But in 43 of Alabama’s 67 counties, the county Probate Courts, which issue the licenses, were not giving them to gay and lesbian couples, according to the Human Rights Campaign, a gay rights group. Many Probate Court judges declined to grant any marriage licenses.

In Florence, in the northwest corner of the state, Judge James Hall of Probate Court explained to Beth Ridley and Rose Roysden that he would not issue a license, saying, “I’m caught up in the middle of this.”

A US District Court judge, Callie V. Granade, ruled last month that Alabama’s ban on same-sex marriage was unconstitutional, but put her ruling on hold until Monday to give the state a chance to appeal. On Sunday night, the state’s chief justice, Roy S. Moore, sent an order to county probate judges stating that they could not “issue or recognize a marriage license that is inconsistent” with state law.

But on Monday morning, the US Supreme Court refused the state’s request to stay Granade’s order pending the outcome of the state’s appeal.

In an interview Monday, Moore, a Baptist who has called marriage “a divine institution ordained by God,” was unapologetic. He asked what would stop judges from redefining marriage in other ways, including potentially allowing polygamy.

“But this is not what this case is about,” he said. “This case is about the federal court’s violation of their own rules.”

In his order to probate judges, Moore cited the state constitutional amendment prohibiting gay marriage and said that he, as chief administrator of the state courts, has authority over the probate courts.

“The argument isn’t crazy, but it’s wrong,” said Noah Feldman, a professor at Harvard Law School who specializes in constitutional issues.