But the group’s commercials all focus on Mr. Rubio. The senator’s picture is prominently featured on its website, and a video featuring Mr. Rubio speaking is the first thing shown to the site’s visitors. The group is now run by Pat Shortridge, an adviser on Mr. Rubio’s 2010 Senate campaign. J. Warren Tompkins, a South Carolina-based Republican consultant who was once a business partner with Mr. Rubio’s campaign manager, is on its board. Mr. Tompkins also oversees the super PAC backing Mr. Rubio — which is called Conservative Solutions PAC and which shares fund-raising consultants with the nonprofit.

Mr. Rubio’s heavy reliance on the group effectively keeps secret the identities of some of his biggest supporters, making it impossible to know whose agenda the senator may be embracing. Mr. Rubio has avidly courted the casino billionaire Sheldon Adelson, for example, even signing on in June as co-sponsor of an Adelson-backed bill that would restrict Internet gambling.

“It doesn’t comport with tax law, but the problem is that the I.R.S. budget has been so constrained that they don’t have a lot of resources in this area,” said Marcus S. Owens, a Washington lawyer who specializes in campaign finance. “So if somebody is comfortable being aggressive, they’re just betting that the audit lottery won’t call their number any time soon, which is probably a safe bet.”

Asked in an interview last week if the group ought to disclose its donors — as he said earlier this year that such groups should — Mr. Rubio initially noted that the group is set up as a nonprofit and that he could not coordinate with them. Pressed on whether he believes they should reveal their funding, Mr. Rubio said: “I think they should follow the law. And if people want to change the law to provide disclosures for groups that participate in the political process, I’m open to that idea, but that’s not the law right now.”

Republican officials have been increasingly reliant on political nonprofits in recent years, as boycotts, public outrage and shareholder activists put pressure on businesses to avoid donating to super PACs. Jeb Bush supporters have created a nonprofit that has a similar name to the super PAC supporting the former Florida governor. But the nonprofit supporting Mr. Bush has yet to air ads.

Democrats have focused more on super PACs to handle their independent expenditures in campaigns, though they also have employed the more secretive 501(c)(4) vehicles. The primary super PAC backing Hillary Rodham Clinton, for example, Priorities USA Action, has not ruled out using its now-dormant nonprofit arm during the 2016 election.