“Speaking for myself personally, it has put me in a difficult position,” Ms. Horton said. “But I am going to uphold the law.” She noted that by midafternoon no same-sex couples had sought licenses at her office.

Image Rebecca Bird, 41, left, and Sandra Quandt, 48, waiting for a marriage license in Davenport, Iowa, on Monday with Ms. Birds sister, Jamie Lee, 28, and niece, Shelbie Stevens, 3. Credit... Amanda Rivkin for The New York Times

Chuck Hurley, the leader of the Iowa Family Policy Center, which opposes such marriages, said he and others were distressed that state lawmakers had adjourned for the year on Sunday without agreeing to begin the process of amending the State Constitution to stop the unions. Mr. Hurley, who delivered a petition with thousands of signatures to the recorder here early Monday, told reporters that more people had not turned out to object because they were busy “raising children and going to work.”

“People I associate with are very much law-abiding people,” he said. “They’re not going to chain themselves to their recorders’ offices.”

Iowa joins Connecticut and Massachusetts in allowing same-sex marriage, and Vermont will follow in September. California also allowed them for about six months until voters there rejected the idea in November.

The Iowa Supreme Court’s ruling on April 3, which surprised many here, spurred a new set of technical, philosophical and legal questions, which public officials and others have been racing to sort through over the past three weeks.

State officials were rushing to change the wording on marriage license applications and other official documents to reflect the change. The forms now refer to “Party A” and “Party B” and give applicants an option to describe themselves as “bride,” “groom” or “spouse.”

Though the court’s ruling had no direct effect on religious leaders, many must decide whether to marry same-sex couples. Members of some denominations are divided on the matter.