AUSTIN, Texas—The legal team for Texas Gov. Rick Perry on Thursday sought to rebut claims that a probe of a state cancer-fighting agency is connected to criminal allegations the governor abused his power.

In a conference call with reporters Thursday morning, lawyers for the Republican governor shared an affidavit from Chris Walling, who said he had been the primary investigator into a criminal probe by the Travis County public integrity unit into the Cancer Prevention and Research Institute of Texas.

The cancer agency, one of Mr. Perry's signature projects, became the subject of a probe last year by the public integrity unit after awarding millions of dollars to projects that allegedly hadn't been thoroughly vetted. Mr. Walling, who no longer works for the public integrity unit, stated in the affidavit that Mr. Perry and his staff were never a target of that probe.

Lawyers for Mr. Perry said they were highlighting the affidavit to counter claims by Democrats that the governor had sought to oust Travis County District Attorney Rosemary Lehmberg, who oversees the public integrity unit, because of concerns about the sensitive investigation.

A grand jury indicted Mr. Perry on Friday on two felony counts in connection with allegedly improperly threatening to veto $7.5 million in funding for the Travis County public integrity unit, which handles political-corruption investigations in Texas, if Ms. Lehmberg didn't resign following a drunken-driving arrest.