Coburn said he was talking to Ensign about his tryst with a former staffer in his capacities as a doctor and a man of the cloth, Roll Call reported.
"I was counseling him as a physician and as an ordained deacon," Coburn said. "That is privileged communication that I will never reveal to anybody. Not to the (Senate) Ethics Committee, not to a court of law, not to anybody."
Doug Hampton, whose wife had engaged in an affair with Ensign, has claimed Coburn urged Ensign to pay the Hamptons millions of dollars after Hampton confronted Ensign about the affair.
"I categorically deny everything he said," Coburn said.
Coburn said he has acted as a counselor to other lawmakers in the past.
"Ya'll don't know about all the people I've counseled," he told Roll Call when asked why Ensign sought his help.
Ensign said Thursday his parents gave $96,000 to his mistress and her family out of concern for the well-being of family friends. In a statement read by his lawyer, Ensign said, "None of the gifts came from campaign or official funds, nor were they related to any campaign or official duties," USA Today reported.
"Sen. Ensign has complied with all applicable laws and Senate ethics rules," the statement said.
Ensign, 51, told the Las Vegas Sun he had no plans to resign.
"I said before, I always planned on serving and working hard -- working harder than I ever worked -- and I'm going to continue to do that," he said.
Celebrity Families of 2014 [PHOTOS]