Rep. Jesse Jackson Jr. (D-Ill.) on Tuesday denied allegations that he instructed a fundraiser to offer then-Gov. Rod Blagojevich (D) campaign cash in exchange for a Senate appointment.

Jackson’s statement was in response to a story in the Chicago Sun-Times, which reported Tuesday that Illinois businessman Raghuveer Nayak made the accusations to federal investigators, according to unnamed sources.

Nayak also alleged he paid for airline tickets for a female acquaintance of Jackson’s at the request of the Illinois lawmaker, the paper reported.

In a statement, Jackson denied wrongdoing and said that he has previously addressed the fundraising claims with federal investigators.

“The allegations about fundraising and the Senate seat are not new,” Jackson stated. “I’ve already talked with the authorities about these claims, told them they were false, and no charges have been brought against me.

“The very idea of raising millions of dollars for a campaign other than my own is preposterous. My interest in the Senate seat was based on years of public service, which I am proud of, not some improper scheme with anyone,” Jackson said.

But Jackson did not directly address the allegations involving the female acquaintance, Giovana Huidobro, identified by the Sun-Times as an employee of the Washington, D.C., martini and cigar bar Ozio.

“The reference to a social acquaintance is a private and personal matter between me and my wife that was handled some time ago. I ask that you respect our privacy,” he said. “I know I have disappointed some supporters and for that I am deeply sorry. But I remain committed to serving my constituents and fighting on their behalf.”

Both Jackson and his spouse, Alderman Sandi Jackson, are among the crowded field of would-be Democratic candidates hoping to replace Chicago Mayor Richard Daley (D), who has announced he will not seek re-election.

The House ethics committee deferred its investigation into related allegations against Jackson in September 2009, citing an ongoing Justice Department investigation.

The Justice Department has not charged Jackson in connection with the case. The Sun-Times reported that Jackson challenged federal prosecutors to “bring it on” in a radio interview last week.

The House ethics committee is expected to announce whether it will continue to defer its inquiry into Jackson or take up the investigation following the November elections.

Both Blagojevich and his brother, Robert Blagojevich, were tried in federal court earlier this year on corruption charges tied to allegations the former governor had attempted to sell the Senate seat previously held by President Barrack Obama.

The jury deadlocked on 23 of 24 charges against Rod Blagojevich and on all four charges against his brother.

The Justice Department has confirmed it will not retry Robert Blagojevich, but the former governor is expected to begin a new trial in early 2011.