The message also featured Adam Gadahn, also known as Azzam al-Amriki, an American who converted to Islam and joined al-Qaeda.
He was charged with treason in 2006 and there is a $1 million reward for information leading to his arrest or conviction.
"The important question is, will Obama and his Democrats learn from his predecessor's mistakes or will they go on repeating them until they too leave office in humiliation and disgrace?" Adam Gadahn said in the video.
"Unfortunately for the Democrats, and judging by their first seven and a half months at the helm of the sinking American ship, the prognosis doesn't look good."
The video also included footage of what appeared to be an American torturing an Afghan for information by dunking his head into a bucket of water.
In his message, al-Zawahiri criticised what he called "the Arab nationalism movement" for being responsible for the situation in Palestine.
He said the election of Mahmoud Abbas as president of Fatah "is considered as a shameless announcement by the nationalism trend to give up its people's rights and turn from a trend of Arab nationalism to that of the international legitimacy, or most appropriately that of the American-Zionist domination".
He condemned a number of Arab countries that have agreed to normalisation of relations with Israel.
The tape comes more than a week after Osama bin Laden warned the US over its close ties with Israel in an audio tape posted on as Islamist website.
Analysts suggested that the posting of Tuesday's tape may have been delayed by nearly two weeks after the anniversary of the September 11 attacks because websites have been jammed or because al-Qaeda is finding it harder to operate.
Bin Laden and al-Zawahiri are thought to be in the mountainous territory along the Afghanistan-Pakistan border, where US forces and the Pakistani military are locked in conflict with groups allied to al-Qaeda.