He reiterated Wednesday that he never participated in a pay-to-play scheme for his appointment to the Senate seat previously held by Barack Obama.
Burris spoke to reporters Wednesday outside his Chicago home before he set out on a two-day tour of central Illinois. The Democrat said he has been truthful at every step since Blagojevich appointed him to the Senate seat.
"Did I try to buy the seat? Never," Burris said. "Did I commit perjury? No."
The Department of Justice released audio of the wiretapped conversation Wednesday evening.
(Read more in CBSNews.com's Political Hotsheet blog.)
"I mean, so Rob, I'm in a dilemma right now wanting to help the governor," Burris tells Robert Blagojevich, who headed his brother's campaign fund, in the phone conversation secretly taped by the FBI.
"I know I could give him a check," Burris says. "Myself. ... I will personally do something, okay."
The senator said Wednesday the check would have been for $1,000, an amount he had donated to the Blagojevich campaign before.
"If you look at the transcript you can see what I was saying," Burris told reporters. "I did not know anything about a pay-to-play. I knew if I raised money, it would be a problem."
On the transcript, Burris had cautioned that "if I put on a fundraiser now ... it has so many negative connotations that Burris is trying to buy an appointment from the governor for the senate seat."
"God knows No. 1, I wanna help Rod," Burris says in the recording. "No. 2, I also wanna, you know, hope I get a consideration to get that appointment."
Perhaps most damaging is Burris' suggestion he might funnel money to Blagojevich thru a third party, reports CBS News correspondent Cynthia Bowers. Burris offered to contribute in the name of a business partner, saying, "I might be able to do this in the name of Tim Wright, okay, because Tim is not looking for an appointment."
Burris' critics say this tape proves Burris lied under oath when he testified at Blagojevich's impeachment hearing he had no contact with the governor's inner circle, a statement later amended to admit he did talk, but never promised anything, Bowers reports.
The transcript of the wiretapped conversation was released Tuesday after U.S. District Chief Judge James F. Holderman approved making it available to the U.S. Senate ethics committee for its preliminary investigation of Burris's appointment.
Burris was at the University of Illinois today for a series of tours and meetings Wednesday. After a tour at the National Center for Supercomputing Applications, Burris reiterated his denial that he'd been involved in any type of pay-to-play scheme regarding his Senate seat.
Burris has been under intense scrutiny since he was appointed by the now-ousted governor at the end of December, and for changing his story multiple times about whether he promised anything in exchange for it. The ethics committee began a preliminary investigation into how Burris got his job, and the Sangamon County State's Attorney was asked to determine whether perjury charges were warranted.
Burris opens the wiretapped conversation by telling Robert Blagojevich: "I know you're calling telling me that you're gonna make me king of the world."
"And therefore I can go off to, you know, wherever and do all these great things," Burris adds. He says that he has "been trying to figure out what the heck, you know, I can do."
"We've had a number of conversations about, you know, anything you might be able to do," Robert Blagojevich says a moment later.
The conversation took place about three weeks before Rod Blagojevich's Dec. 9 arrest on charges of scheming to sell or trade the Senate seat being vacated by President Barack Obama's election and using the political muscle of the governor's office to squeeze people involved in state business for campaign contributions.
Blagojevich and his brother have both pleaded not guilty in response to charges in the case as have four other members of the former governor's inner circle.
Neither Robert Blagojevich's attorney, Michael Ettinger, nor Burris attorney Timothy Wright objected to the government's motion to give the tapes to the Senate. Wright said Tuesday that Burris never wrote any checks to the Blagojevich campaign following the conversation.
A spokesman for the U.S. attorney's office, Randall Samborn, had no comment.
The former governor, ousted by lawmakers in January, has been the focus of a federal corruption investigation for years.
He was indicted in April on charges of scheming to trade or sell Obama's old seat and using the political muscle of his office to squeeze people for campaign money. Also indicted were Robert Blagojevich, former campaign fund chairman Christopher G. Kelly, former Blagojevich chiefs of staff John Harris and Alonzo Monk and Springfield multimillionaire William Cellini.
All have pleaded not guilty, although Harris's attorney says he is cooperating with federal prosecutors and Monk is believed to be as well.
Burris' Senate appointment followed at least two phone conversations between Burris and Robert Blagojevich.
Burris told the Illinois House impeachment committee that he had promised nothing to Blagojevich in exchange for the seat but has changed his version of exactly what was said several times and questions have been raised about what happened.
U.S. Sen. Dick Durbin, D-Ill., and Senate Majority Leader Harry Reid, D-Nev., agreed to seat Burris if he gave a full accounting of his Blagojevich contacts to the Illinois House committee that considered impeachment of the governor.
Burris gave the committee an affidavit denying any discussion with Blagojevich's aides before being offered the seat. But when he testified, Burris acknowledged talking to one of Blagojevich's friends and informal advisers about it.
In a further blow to Burris' standing, Illinois House Republicans are now calling for him to resign.
They have introduced a resolution calling for him to quit the job. House Republicans tried to get immediate action on the resolution Wednesday, but the Democratic majority wouldn't agree to put it on a fast-track.
Burris did not admit talking to anyone else and said he could not recall any other contacts.
Then, after he was sworn in, Burris released another affidavit acknowledging that he had talked to several Blagojevich advisers about his interest in the seat. Soon after, talking to reporters, he said he had been asked to help raise campaign money for the governor and tried to find people willing to donate but failed.