In the tape, played on Saturday, the man blamed by the US for organising the September 11, 2001 attacks gave separate messages to listeners in Iraq and in the US.
To the US, he issued a stark warning that his followers would carry out further actions both inside and outside the United States.
"We, God willing, will continue to fight you and will continue martyrdom operations inside and outside the United States until you abandon your oppression and foolish acts," he said.
He also addressed the American people, accusing them of electing an "evil" leader.
"Bush has sent your sons into the lion’s den, to slaughter and be slaughtered, claiming that this act was in defence of international peace and America’s security, thus concealing the facts."
To Iraqis, he encouraged resistance against the US-led forces that had ousted former leader Saddam Hussein and taken control of the war-ravaged country.
He saluted groups that had carried out attacks on the occupying coalition forces, which include soldiers from Spain, Britain, Poland and Australia, as well as the US.
He also threatened others such as those Gulf states that allowed their territories to be used as a launchpad for attacks against Iraq, especially Kuwait.