But, he told reporters on Sunday, "If somebody in the Bush campaign keeps sending confidential internal data to us, we'll keep turning it over to the FBI."
That comment, in a conference call with reporters, came as the two camps traded new accusations over the mysterious package and whether there is a Gore spy in Bush's campaign.
Bush operatives seized upon the Gore campaign's suspension of a junior staffer in the matter to hurl new accusations at Gore's Nashville-based operation.
"The more the FBI inquires, the more nervous they're getting in Nashville," said Bush spokesman Ari Fleischer.
The Gore staffer, Michael Doyne was suspended after he acknowledged boasting of a "mole" planted in Bush's campaign.
The 28-year-old Doyne now insists the "mole" was a product of his imagination - and Gore spokesman Mark Fabiani said campaign officials do not believe there is any such Democratic spy.
But Fleischer said Doyne's suspension "raises questions on whether others in the Gore campaign have information" obtained through political espionage.
"It defies credibility," Fleischer said of the whole incident.
GOP running mate Dick Cheney said there's cause for concern. "There seems to be a little bit of smoke there. Whether or not there's a fire, I don't know," he said on ABC's This Week.
On Sept. 13, a package including the tape arrived at the Washington office of former Rep. Thomas Downey of New York, who had been helping Gore prepare for the debates. It had an Austin, Tex. postmark.
Gore told reporters that Doyne "has signed a sworn affidavit that he has no knowledge whatsoever of any so-called mole or Gore sympathizer within the George Bush presidential campaign. That's all I know about it."
As to the tape, "I don't know who sent it," Gore said. "I've read the reports that the FBI has identified a Bush campaign official as the person responsible but I have no knowledge other than that."
Bush campaign officials have denied strongly that anyone involved in debate preparations sent the tape to Gore's campaign.
However, they have not ruled out the possibility that a junior staffer may have stumbled upon a copy of the tape and passed it on - or that a security lapse may have allowed the tape to be copied outside campaign headquarters.