The rule in question has been adopted by the agency, but its implementation was suspended nationally in October by a federal appeals court after opponents of the plan challenged it.

The G.A.O. report details two specific violations that took place as the E.P.A. was preparing to issue the final rule. The first involved the Thunderclap campaign in September 2014, in which the E.P.A. used a new type of social media tool to quickly reach out to 1.8 million people to urge them to support the clean-water proposal. Thunderclap, described as an online flash mob, allows large groups of people to share a single message at once.

“Clean water is important to me,” the Thunderclap message said. “I support E.P.A.’s efforts to protect it for my health, my family and my community.”

The effort violated federal law, the G.A.O. said, because as it ricocheted around the Internet, many people who received the message would not have known that it was written by the E.P.A., making it covert propaganda. The E.P.A. disputes this finding, noting that it sent out the original Thunderclap message and was hardly hiding its role.

The agency is also said to have violated the anti-lobbying law when one of its public affairs officers, Travis Loop, wrote a blog post saying he was a surfer and did not “want to get sick from pollution.” That post included a link button to an advocacy group that discussed the danger that polluted water posed to surfers and, at least at one point, also included text that said “Take Action,” telling the public to “tell Congress to stop interfering with your right to clean water.”

Such findings by the G.A.O. are infrequent but not without precedent. During George W. Bush’s administration, the G.A.O. concluded similarly that the Centers for Medicare and Medicaid Services violated the anti-propaganda act in 2004 when it covertly paid for news videos distributed to television stations without disclosing that the government had financed the work. In 2005, the Department of Education was found to have violated the same law when it hired a public relations firm to covertly promote the No Child Left Behind Act of 2001.

The entire amount spent on the social media campaign in question is likely trivial. But whatever the cost, the G.A.O. asserted that it violated a federal Antideficiency Act, which prohibits federal agencies from spending money without authorization. Penalties include fines and even possible jail time. But even Republicans on Capitol Hill say it will not be enforced that way.