He also vowed more attacks against the United States in the Middle East and Africa.
Bin Laden calls Zarqawi both a "prince" and a "lion of the holy war" in his 19-minute tribute to al-Zarqawi, CBS News correspondent Richard Roth reports. Bin Laden also said the former al Qaeda in Iraq leader had been under orders to kill Iraqis who supported U.S. forces in the country.
"We will continue to fight you and your allies everywhere, in Iraq, Afghanistan, Somalia and Sudan to run down your resources and kill your men until you return defeated to your nation," he said, addressing Mr. Bush. His voice sounded breathy and fatigued at times.
The clear implication in the message, Roth reports, is that there's no dispute within al Qaeda about terror tactics, and there's no question that bin Laden is still in charge.
Although a new video of the terrorist leader has not been seen since October 2004, this was the fourth audio message purportedly put out this year by bin Laden. The voice in the latest message — released on an Islamic Web forum where militants often post messages — resembled that on previous recordings attributed to bin Laden, but the authenticity of the tape could not be immediately confirmed.
Al-Zarqawi was killed in a June 7 airstrike northeast of Baghdad by U.S. warplanes. Bin Laden said Mr. Bush should return al-Zarqawi's body and that Jordan's King Abdullah II should allow the militant's family to bury him.
The Jordanian government has said it will never allow al-Zarqawi to be buried in his homeland because of a November triple suicide bombing his followers carried out in Amman hotels that killed 60 people.
"What scares you about Abu Musab after he's dead?" bin Laden said, addressing Abdullah. "You know that his funeral, if allowed to happen, would be a huge funeral showing the extent of sympathy with the mujahedeen."
The audio message was accompanied by a video showing an old photo of bin Laden next to images of al-Zarqawi taken from a previous video.
The message bore the logo of As-Sahab, the al Qaeda production branch that releases all its messages. Typically, the CIA does a technical analysis to determine whether the speaker is who the tape claims and the National Counterterrorism Center analyzes the message's contents.
Since the discovery of the new message, the hunt for Zarqawi's successor has only intensified, CBS News correspondent Lee Cowan reports. Friday morning both U.S. And coalition troops mounted a raid just north of Baghdad. It ended up in a fire fight, CBS News has learned.
According to Cowan, there's no word on any U.S. casualties, but at least three insurgents were killed and several more were captured.
In the tape, bin Laden effusively praised the Jordanian-born al-Zarqawi, often in rhyming couplets.
"Al-Zarqawi's story will live forever with the stories of the nobles, so don't cry over one who is not missing," bin Laden said. "He can teach the world a lesson on how to seize freedom ... and how to resist tyrants."
The tape comes exactly a week after bin Laden's deputy Ayman al-Zawahri issued his own tribute video to al-Zarqawi, extolling him as "the prince of martyrs."
The tributes appear to be part of an attempt by al Qaeda's leadership to tout their connection to al-Zarqawi, who emerged as a hero among Islamic extremists with his dramatic attacks in Iraq and even stole the spotlight from bin Laden and al-Zawahri.
Al-Zarqawi had sworn his allegiance to bin Laden, the terror network's overall leader, but often had tense relations with him and al-Zawahri. In July 2005, al-Zawahri reportedly wrote a letter to al-Zarqawi criticizing his attacks on Iraqi Shiite mosques and civilians, saying they hurt the mujahedeen's image.
The al Qaeda deputy also asked al-Zarqawi for money, according to the U.S. military, which said it intercepted the message.
Al-Zarqawi apparently brushed off the criticism as he continued to attack Shiites, a strategy intended to spark a Sunni-Shiite civil war.
In the new tape, bin Laden addressed "those who accuse Abu Musab of killing certain sectors of the Iraqi people," referring to the campaign of suicide bombings against Shiites.
"Abu Musab had clear instructions to focus his fight on the occupiers, particularly the Americans and to leave aside anyone who remains neutral," bin Laden said.
"But for those who refused (neutrality) and stood to fight on the side of the crusaders against the Muslims, then he should kill them whoever they are, regardless of their sect or tribe. For supporting infidels against Muslims is a major sin."
Bin Laden's mention of "instructions" to al-Zarqawi could be aimed to show the al Qaeda in Iraq leader was under his command.
"I hope it redefines and redirects our campaign against bin Laden," CBS News terrorism analyst
Bin Laden and al-Zawahri are believed to be hiding in the rugged border zone of Pakistan and Afghanistan.
"In conclusion, I say that Abu Musab was not just an honor to his tribe, his country and his Islamic nation, but to all mankind, for he embodied the meaning of pride and glory," bin Laden said.