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.
The payments were made to Cynthia Hampton, her husband, Doug, and their two children, the newspaper said. Cynthia Hampton was had been treasurer for two Ensign-controlled campaign committees.
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.
Doug Hampton said Ensign paid more than $25,000 in severance pay when Cynthia Hampton left her job on Ensign's campaign staff in May 2088, the Las Vegas Review-Journal reported.
Doug Hampton was a senior staffer in Ensign's Senate office until May 2008. He claims both he and wife lost their jobs with the senator because of the affair. He also alleged several of Ensign's friends, including Sen. Tom Coburn, R-Okla., urged Ensign to given the Hamptons a huge financial payment -- "millions of dollars" -- and end the relationship.
The Review-Journal said Ensign spokesman Tory Mazzola issued a statement saying, "Ensign said Doug Hampton was consistently inaccurate in his statements."
Coburn's office confirmed he knew about Ensign's affair and had urged him to end it, Politico reported. However, Coburn spokesman John Hart said the senator "categorically denies" Hampton's claim that he urged Ensign to pay millions to the couple.
Coburn said Thursday he would invoke privilege if asked about advice he gave to Ensign on handling the extramarital affair. Coburn said he had talked to Ensign in his capacities as a doctor and an ordained deacon, Roll Call reported.
2014: The Year in Music [PHOTOS]