Morenatti was seized as he headed out of his Gaza City apartment for an AP car, where Majed Hamdan, an AP driver and translator, was waiting. Hamdan said four gunmen grabbed his keys and cell phone and told him to turn away, pressing a gun to his head and threatening to harm him if he moved.
They took Morenatti, shoving him into a white Volkswagen Golf and driving off, Hamdan said.
Hours later, Morenatti was turned over to Fatah forces.
Abbas is not in Gaza, but his office is a safe Fatah stronghold in the territory, which is in the throes of a sometimes violent power struggle between Abbas' Fatah and the militant Islamic Hamas, which is in charge of the Palestinian government.
In the past two years, militants have frequently kidnapped foreigners as bargaining chips to get relatives released from Palestinian prisons, secure government jobs or settle personal scores. In most cases, the kidnappings were brief and the hostages released unharmed.
But recently, the kidnappers have changed tactics. Two Fox News journalists kidnapped in August were held for two weeks, much longer than previous cases. The men also suffered physical and mental abuse in captivity.
An unknown group calling itself the Holy Jihad Brigades claimed responsibility for the August abduction, and its demand for the release of Muslim prisoners held by the U.S. raised fears that foreign extremists, perhaps al-Qaida, had infiltrated Gaza. But Palestinian security officials said the name was a front for local militants.
The media advocacy groups Reporters Without Borders and the Committee to Protect Journalists condemned Morenatti's kidnapping.
"We're dismayed that journalists have become pawns of Palestinian groups seeking to exploit them for political purposes," said CPJ Executive Director Joel Simon. "These blatant attacks on journalists will have a chilling effect on their ability to do their work and will ultimately deprive the world of information about this critically important story."
Morenatti, from Jerez, Spain, has been based in Jerusalem since April 2005, handling periodic assignments in Gaza and the West Bank. He has been in Gaza since Sunday.
Morenatti began working for the AP in April 2004, and spent a year in Afghanistan covering the conflict there. He also covered the war in Lebanon and the World Cup soccer tournament in Germany.
In 1992, Morenatti began work as a photographer with EFE, the Spanish news agency, Spain.
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