The White House is fighting back against Rep. Mark Kirk's (R-Ill.) allegation that the administration leaked information about Kirk's military record.

Kirk made the accusation with "no evidence," the Chicago Sun-Times reports, and White House adviser David Axelrod said Thursday is not true.

"Obviously, Congressman Kirk has some problems that are of his creation, and he can't download them on us," Axelrod told the paper. "I assure you that everyone here has plenty to do. No one is trafficking in revelatory records about him."

Kirk, who's running for President Barack Obama's former Senate seat, has been damaged by a series of revelations about his military career.

The White House has come under fire for involvement in other Senate races, including allegations it made job offers to candidates in Pennsylvania and Colorado to encourage them not to run. Administration officials also got involved in the New York Senate race, helping to clear the primary field for Sen. Kristen Gillibrand (D-N.Y.)

The Kirk campaign told the paper they will file a Freedom of Information Act (FOIA) for all correspondence between "administration officials and Democratic campaigns or political operative regarding Mr. Kirk's personal military records."

The White House isn't covered by FOIA and neither are the campaign committees, the Sun-Times points out.

The latest poll on the race, released Wednesday, shows it's a close one. Kirk leads Democrat Alexi Giannoulias by three points, according to Rasmussen Reports.