The speaker on the tape was identified as Abu Hamza al-Muhajir, also believed to use the name Abu Ayyub al-Masri.
He became the leader of al-Qaeda in Iraq after the killing of his predecessor Abu Musab al-Zarqawi in a US air strike in June.
"Place your hands in our hands ... our enemy has unified his ranks, now is the time to unite," said the speaker on the tape.
The speaker urged Islamists to "kill at least one American within a period not exceeding 15 days".
Al-Muhajir was announced as al-Qaeda in Iraq's new leader on June 12 and received Osama bin Laden's endorsement in an audiotape from the al-Qaeda chief.
In the first major attack claimed by the group under al-Muhajir, it said it carried out the kidnapping and slaying of two American soldiers whose mutilated bodies were found in southern Baghdad on June 20.
Al-Qaeda in Iraq accounts for about 5 per cent of Iraq's Sunni Arab uprising but its bombers have been responsible for some of the worst violence, often killing over 100 people in a single attack.