SPRINGFIELD, Ill. (AP) — Senate candidate Mark Kirk pushed back Tuesday against a Pentagon statement that he improperly mixed politics with his service in the Navy Reserve, while his Democratic opponent said Kirk wasn't being truthful.

The Defense Department said it has twice warned Kirk after incidents in which he conducted political business while on duty — once by giving interviews about the arrest of former Illinois Gov. Rod Blagojevich and once by posting a Twitter statement about his work at the Pentagon.

"Commander Kirk was counseled about both of the incidents," according to a statement provided by Pentagon spokeswoman Maj. April Cunningham late Monday night.

The Kirk campaign last week denied he had ever improperly mixed politics with his military service, and the Republican seemed to stick to that position Tuesday despite the Pentagon statement.

"The campaign has made all of the congressman's military fitness reports available for review and no concerns were documented," Kirk spokeswoman Kirsten Kukowski said in a statement.

Kukowski did not immediately respond to a message seeking additional comment.

But Democrat Alexi Giannoulias quickly addressed the issue.

A statement from his campaign said Kirk was "not being truthful."

Giannoulias, the state treasurer, said in a conference call with reporters that the Pentagon statement "raises grave questions."

"I think this ... begs the question of what else in his professional career is Mark Kirk not telling the truth about," Giannoulias said. "I think there are a lot of voters who want to hear Mark Kirk's answer on this latest development."

Kirk, a five-term member of Congress from Chicago's northern suburbs, is battling Giannoulias for the Senate seat once held by President Barack Obama.

Kirk has made his 21 years of service in the Navy Reserve a key part of his campaign, mentioning it in most speeches and news releases.

But that was before revelations that he had exaggerated his military record, particularly by repeatedly saying he was named intelligence officer of the year. The award in question went to his entire unit.

The issue of Kirk taking political action while on active duty was first raised when a blogger named Terry Welch disclosed a Defense Department memo on the issue.

The Kirk campaign said then that he had "never" violated Pentagon policy.

"The document in question should be viewed for what it is — a baseless political ploy by partisans bent on defending a U.S. Senate seat at any cost," Kukowski said last week.

But the Defense Department said Kirk violated policy twice.

In late 2008, Kirk gave video interviews about Illinois Gov. Rod Blagojevich being arrested, the Pentagon statement said. The Kirk campaign counters that regulations allowed him to conduct business related to his congressional duties.

And in July 2009, Kirk or a staff member wrote on the candidate's Twitter account that he was on duty at the Pentagon's National Military Command Center.

The Defense Department required Kirk to sign a statement acknowledging that political activity is not permitted while on active duty before he was given permission to return to Afghanistan in December 2009.