The statement did not name a successor to Zarqawi, who was killed by a U.S. airstrike Wednesday. But it said the group's leadership "renews its allegiance" to Usama bin Laden.
Bin Laden "will see things that will bring joy to his heart," it said, vowing "to prepare major attacks that will shake the enemy like an earthquake and rattle them out of sleep."
The authenticity of the statement could not be independently confirmed. It was posted on an Islamic militant Web forum where the group has posted statements in the past.
The statement was issued in the name of Al Qaeda in Iraq but was put out by the Mujahedeen Shura Council, an umbrella organization of five insurgent groups that Zarqawi helped create.
The statement said Al Qaeda in Iraq's leadership met after Zarqawi's death and "agreed to continue jihad [holy war] and not be affected by his martyrdom."
"The organization has strengthened its back, regained its footing and has been renewed with fresh blood," it said, listing previous prominent members who had been killed without setting back the group's attacks.
"For those who were waging holy war for the sake of al-Zarqawi, al-Zarqawi is dead. But for those who were fighting for the sake of God, God is alive and eternal," it said.
The phrase echoed the words used by the Prophet Muhammad's successor, Abu Bakr, after the prophet's death in the 7th century to urge Muslims to stick to their new faith.
The message left unknown the issue of who will succeed Zarqawi as the group's "emir," or leader.
Thursday's Al Qaeda statement was signed by Zarqawi's deputy emir, Abu Abdul-Rahman al-Iraqi, and sympathizers quickly flooded Web forums with vows of allegiance to him.
But Sunday's message did not mention his name. There is confusion over whether he is still alive, after the U.S. military said a man named "Abdul-Rahman," whom it identified as Zarqawi's spiritual adviser, died in the airstrike alongside his leader.
The U.S. military has said the mostly likely successor is an Egyptian associate of Zarqawi named Abu Ayyub al-Masri, who has a $50,000 reward on his head.