According to a CNN translation of the tape, bin Laden also declares "Our flag has not fallen".
CNN said that in the 19-minute 32-second tape, posted on an Islamic website often used by al-Qaeda but which it did not identify, bin Laden addressed US President George W Bush, saying that Zarqawi's body should be returned to his native Jordan.
The voice continues: "The lion of jihad ... Abu Musab al-Zarqawi ... was killed in a US raid. We hope to God he accepts him as a martyr".
The authenticity of the tape could not be immediately verified, but US intelligence officials said it was conducting tests.
"US intelligence is conducting technical analysis on the new tape, but at this point there is no reason to doubt it is real," said a US counter-terrorism official.
"This is part of al-Qaeda's ongoing propaganda campaign and part of bin Laden's effort to demonstrate that he is still relevant."
Earlier this month, al-Qaeda's second-in-command Ayman al-Zawahri vowed vengeance against the United States for the death of Zarqawi in a videotape.
Last month, bin Laden released an audiotape saying that Zacarias Moussaoui, the only person convicted in a US court for the September 11, 2001, terrorist attacks on the US, had nothing to do with the operations.