In the video posted on militant websites, Ayman al-Zawahri called America a "criminal country" that has corrupted the world.
"Chase America, which killed the leader of the mujahedeen and threw his body into the sea," he said. "Go after it so that history will say that God enabled his worshippers to attack a criminal country which has spread corruption in the world."
The 12-minute message is the third from the Egyptian-born al-Zawahri since he was named al Qaeda's new leader in June following the killing of bin Laden.
Al-Zawahri also said the uprisings in Egypt and Tunisia have provided opportunities for the group to spread its message.
"In Tunisia and Egypt, opportunities for preaching have been opened and only God knows until when these opportunities will last," he said. "Therefore, the Muslims and the mujahedeen should benefit and take advantage of them to reveal the truth."
The video was released about four weeks before the 10th anniversary of the Sept. 11 attacks.
The Associated Press contributed to this report.