Chief Justice Roy Moore said judges were not bound by a federal ruling lifting the state's gay marriage ban.
But at least three counties have begun issuing licences after the US Supreme Court refused to put marriages on hold.
Other counties have said they will not marry any couple, according to local media.
|James Dansby protests in front of the Jefferson County courthouse as same-sex |
couples wait for the doors to open so they can be legally married in Birmingham,
Alabama, 9 February 2015
But on Monday morning, he was powerless to stop the state becoming the 37th to issue marriage licences.
In Birmingham, one of the first licenses went to Dee and Laura Bush, who have been together for seven years and have five children between them. I wonder what God thinks about lesbian couples having children? I would think that if He wanted that to happen He would have made a way for it to happen naturally. What a dreadful time it is when we find so many ways to subvert God's desires for us.
They wed in a park outside the courthouse where a minister was performing ceremonies.
"It is great that we were able to be part of history," said Dee Bush.
Judges elsewhere were wary or defiant following the federal ruling.
|Alabama Sanctity of Marriage holds a rally at the State Capitol Building|
in Montgomery on 7 February
"There's a conflict, and I want to follow the law," Judge Rosser said. "But it is difficult this morning to follow the law."
One county judge refused to issue any licence not between "one man and one woman only, so help me God", while others declared they would not be marrying any couple - gay or heterosexual.
|Gay rights campaigners have been urging judges not to follow|
Chief Justice Roy Moore's directions
The order was put on hold until 9 February to let the state prepare for the change.
It was the latest in a wave of similar federal rulings across the United States.
In November, however, a federal appeals court based in Cincinnati decided to uphold bans on gay weddings in Kentucky, Michigan, Ohio and Tennessee.
The conflicting rulings among the appeals courts have prompted the US Supreme Court to hear the case later in the year.