Through a team spokesperson, the Rays declined to comment on Selig's remarks.
Tampa Bay's average home attendance of 17,790 ranks 29th out of 30 teams in the Majors, ahead of the Marlins' average of 17,416. Selig said that he remains in regular contact with Rays principal owner Stu Sternberg.
"I think his patience is running as thin as mine is," Selig said. "He and I have had conversations within the past 24 hours, and we'll have another one today."
In an interview last month with FOXSports.com, Sternberg said he feels "better" about the Rays' stadium stalemate than he did last year, but also that "at some point in the next few years, we've got to have it figured out."
Selig said there was "no question there's a stadium problem there" and that he will continue to discuss the matter with Sternberg until a solution is found.
Selig noted that Tampa Bay's attendance issues are particularly problematic considering the club has won at least 90 games in four of the past five seasons. The Rays are 55-41 this year, second in the American League East, but their average attendance falls below the league average of 30,226.
"Look at a club in the Major Leagues that's competitive and is averaging 18,000 people a game. That may have been OK in 1956. It's not OK today," Selig said. "Your fans want you to be competitive. Well, they ought to have the economic tools or the economic mechanisms to be competitive. You can't say they've run a poor franchise. They've run an extraordinary franchise. Every year, they lose a lot of players and they just keep on going.
"The question is what to do about it, and where and when."
Adam Berry is a reporter for MLB.com. National columnist Mike Bauman contributed to this story. Follow Adam on Twitter at @adamdberry. This story was not subject to the approval of Major League Baseball or its clubs.