Al-Zarqawi, a Jordanian who masterminded hundreds of bombings, kidnappings and beheadings in Iraq, was killed June 7 in an U.S. airstrike north of Baghdad. He was al Qaeda's leader in Iraq.
On the tape, bin Laden addresses President Bush directly and demands that the U.S. return al-Zarqawi's body to his family in Jordan.
"I say to Bush, you should deliver the body (of al-Zarqawi) to his family, and don't be too happy. Our flag hasn't fallen, thanks be to God. It has passed from one lion to another lion in Islam," the message in Arabic says, according to a translation by Octavia Nasr, CNN's senior editor for Arab affairs.
"We will continue, God willing, to fight you and your allies everywhere, in Iraq, Afghanistan, Somalia and Sudan, until we drain your money and kill your men and send you home defeated, God willing, as we defeated you before, thanks to God, in Somalia."
The U.S. government has never given a public accounting of what happened to al-Zarqawi's body after the autopsy.
"I say to your agent (King Abdullah) in Jordan, stop your tyranny. You have prevented Abu Musab from entering his homeland alive, don't stand in his way now."
Jordanian courts convicted and sentenced al-Zarqawi in absentia after he admitted to the Nov. 11, 2005, triple hotel bombings in Amman that killed 60 people and injured scores, mostly Jordanians.
Although CNN cannot independently verify that the voice in the message is bin Laden's, several experts have told CNN it appears to be.
Another section of the message says, "Our dear Muslim nation, we were deeply saddened by the passing of our loved ones, Abu Musab and his companions, but we were very happy that their souls have flooded these great battles as they were defending the Islamic law."
Al-Zarqawi was killed "following a hateful American raid," the al Qaeda leader says.
Bin Laden refers to al-Zarqawi as "one of our greatest knights and one of our best emirs (leaders)," and adds, "We were very happy to find in him a symbol and role model for our future generations."
In the message, bin Laden refers to al-Zarqawi by his given name -- Ahmed al-Khalayleh -- a sign of respect, Nasr said.
The audio message, which last 19 minutes, 32 seconds, is imposed over a split screen, with a still photo of bin Laden on one side and a video of al-Zarqawi on the other.
On Wednesday, the Web site, which often posts messages, statements and videos from al Qaeda, posted a note saying it was expecting a message "soon" from bin Laden.
The site posted a nearly identical notification last Thursday on behalf of al Qaeda's second-in-command, Ayman al-Zawahiri. The following day, a videotape was aired on the Arab network Al-Jazeera in which al-Zawahiri said he was grieving the death of al-Zarqawi.
The last audio Web site message purportedly from bin Laden was May 23, when he said that neither Zacarias Moussaoui nor any of the prisoners held at the U.S. Navy detention center at Guantanamo Bay, Cuba, had anything to do with the Sept. 11, 2001, terrorist attacks.