US special forces killed bin Laden in a raid on the Pakistani city of Abbottabad on May 2.
Al-Qaeda under the new leadership of al-Zawahiri will pursue its fight against the US and Israel, the group said in the statement.
"We seek with the aid of God to call for the religion of truth and incite our nation to fight ... by carrying out jihad against the apostate invaders ... with their head being crusader America and its servant Israel, and whoever supports them," it said.
Al-Zawahiri has been al-Qaeda's number two for years.
In the News Stories at al-jazeera , We Found That Al-zawahiri`s name is as Familiar As Osama Bin Laden:
$25 Million United State Dollar Bounty
His whereabouts are unknown but he is widely believed to be hiding along the border between Afghanistan and Pakistan. The United States is offering a $25m reward for any information leading to his capture or conviction.
"Only a few weeks ago when the US Secretary of State Hillary Clinton was here in Pakistan she reportedly gave Pakistan what's been described as a hitlist", Al Jazeera's Imtiaz Tyab, reporting from Islamabad, said.
"It listed five names and Zawahiri's name was on the list. Whether that means the new al-Qaeda leader is here we don't know for sure, but it certainly raises some questions".
Believed to be in his late 50s, al-Zawahiri met bin Laden in the mid-1980s when both were in Pakistan to support fighters battling the Soviet Union in Afghanistan.
Ayman al-Zawahiri New Al-Qaeda`s Leader Following the Killing Of Osama Bin Laden
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