Bin Laden specifically referenced the two leading candidates for president, saying American security relied not on who won Tuesday but on the United States changing its foreign policy.
"Your security is not in the hands of Kerry, or Bush or al-Qaida. Your security is in your own hands," bin Laden said. "Each state that does not mess with our security, has naturally guaranteed its own security."
U.S. officials confirmed intelligence experts believed the tape was authentic and made recently.
President Bush addressed the tape before boarding Air Force One while campaigning in Toledo, Ohio.
"America will not be intimidated or influenced by an enemy of this country. I am sure Senator Kerry agrees with that," the president said in brief remarks. "We are at war with these terrorist and I am confident we will prevail."
Senator Kerry, spending the day campaigning in the battleground state of Florida, said the tape reaffirmed his commitment to focus the American military and intelligence efforts on catching or killing the fugitive Saudi.
"In response to this tape of Osama bin Laden, let me make it clear, crystal clear, as Americans we are absolutely united in our determination to hunt down and destroy Osama bin Laden and the terrorists," the senator told reporters.
"They are barbarians and I will stop at absolutely nothing to hunt down and capture or kill the terrorists wherever they are, whatever it takes. Period."
Democratic operatives also blasted the tape as "an outrageous attempt to intimidate" the United States, Richard Holbrooke, former diplomat and Kerry campaign adviser, told CNN Friday.
"We have a real problem on our hands three years after Sept. 11th," Holbrooke told CNN anchor Wolf Blitzer. "The tape shows he is still around."
Danielle Pletka accused Holbrooke on CNN for "exploiting" the tape for political gain, calling it astonishing that the former U.N. ambassador was "using threats against the United States and the American people to help his candidate."