David Hearn, a former Olympic canoeist who was accused of vandalizing the Lincoln Memorial Reflecting Pool last month, pleaded not guilty on Thursday to a felony charge of destruction of property worth more than $1,000.

Mr. Hearn, 67, was one of at least four people who were arrested in June after the police said they peeled paint off the floor of the reflecting pool, which recently underwent a costly renovation project that has faced numerous problems. Mr. Hearn previously said he had visited the pool simply to take a look at it and, out of curiosity, reached down to touch a strip of peeling blue paint.

“If he can be charged with a felony for touching the reflecting pool, every American is at risk,” one of Mr. Hearn’s lawyers, Norm Eisen, said outside the courthouse on Thursday. “Every American should be alarmed about this prosecution.”

President Trump has blamed vandals for the problems at the pool, including green algae and the peeling liner. He has said that people poured fertilizer into the water to nurture the algae and slashed the blue coating on the pool’s bottom, but he has not cited any evidence to support that claim, and Mr. Hearn has not been accused of either of those things.

The peeling could also be a result of the type of material that was used to coat the pool, according to a review by The New York Times.

Mr. Hearn, who did not speak during the arraignment aside from giving his name, was released on Thursday without bail and was ordered to reappear in court on Aug. 5. Prosecutors asked Associate Judge Carmen McLean of D.C. Superior Court to order that Mr. Hearn stay away from the reflecting pool, but she declined to do.

“Mr. Hearn is 67 years old and an upstanding citizen and member of the community,”Mary Dohrmann, another lawyer representing Mr. Hearn, said in court, adding that “he’s a three-time Olympian who regularly represents the United States in athletic competitions across the globe.”

Outside the courthouse on Thursday, a few dozen demonstrators marched in support of Mr. Hearn and chanted “Davey! Davey!” as Mr. Hearn left the courthouse.

Seven people, including Mr. Hearn, have been arrested on charges of vandalism, federal officials have said. Three people face misdemeanor charges of destruction of property under $1,000, court records show. One of the three declined to comment and the other two could not be reached. It is unclear who the other three people are and what they have been charged with.

The renovation of the pool, at an estimated cost of $16.4 million, has involved upgrading a water-purification system, sealing leaky joints between the pool’s concrete slabs and coating the slabs with a waterproofing material in a color Mr. Trump has called “American flag blue.” The administration awarded no-bid contracts, saying they needed to expedite the project to have it completed by the nation’s 250th birthday party on July 4.

But after officials removed devices used to combat algae, the water turned from blue to green and enormous algae blooms began to spread unchecked.