In at least three counties, couples made the request on Wednesday and were told Tennessee law doesn't recognize same-sex marriages.
The Tennessean reported Will Peyton and Jef Laudieri of Nashville left the Davidson County Courthouse empty handed.
Stephanie Shelton and Lisa Cross of Mt. Juliet tried unsuccessfully to get a marriage license in Wilson County.
Amy Barton, and Lyndsay Gray walked away from the clerk's office without an application on Wednesday, according to The Commercial Appeal. So did Aaron Thompson and Chris Snow.
Davidson County Clerk Brenda Wynn said she prepared a statement for workers in the office to read from, expecting there would be couples asking for marriage licenses.
Payton and Laudieri stood before Tara Marks' desk as she read from the statement, saying, "Tennessee statute prohibits marriage between two people of the same sex."
Laudieri thanked Marks for her time and he and Peyton left.
The coordinated action was intended partly to raise awareness about the inability of lesbian, gay, bisexual and transgender couples to marry in their home state.
In Memphis, where Barton and Gray applied, Gray indicated the effort will continue.
"Somebody has to be denied before they can do anything," she said.
The requests follow the U.S. Supreme Court ruling that gives gay couples who are legally married in states that allow it equal federal footing with all other married Americans.
In Tennessee, however, marriage between partners of the same gender is prohibited by state law and constitutional amendment.
State Rep. Glen Casada, R-Franklin, said most of his constituents have other concerns that defining marriage.
"The people of Tennessee want to define marriage as a man and a woman," Casada said. "I think that the Republicans would want to do the wish of 80 percent of the people of Tennessee, which is honor the constitution as written.
The amendment to the state constitution was passed in a 2006 referendum.
But Nashville attorney Abby Rubenfeld, who married under California's same-sex marriage statute, said Tennessee gays will eventually prevail in court and foresees an end to so-called defense of marriage acts.
"I think we have pretty decent courts, the law is really clear, the Supreme Court decision was very clear," Rubenfeld said. "Even (Justice) Scalia, in his dissent, said he felt it meant the end of all the state DOMAs."