Emilio Morenatti, 37, was seized by four armed and masked men as he left an agency apartment in Gaza City early morning and bundled into a waiting car.
No group immediately claimed responsibility for the kidnapping, the latest in a string of abductions of foreigners in the increasingly lawless Gaza.
"We demand the kidnappers release him immediately," a spokesman for the Hamas, Ghazi Hamad, told AFP.
"We strongly condemn this kidnapping and we are doing all we can to free him," he said. "This kidnapping is in contradiction to our national interests and blackens the image of Palestinians."
Hamas did not know who carried out the kidnapping or their motivations, Hamad said.
In Ramallah, Abbas's office also blasted the kidnapping.
"We condemn this kidnapping and we call for the kidnappers to release him immediately," said a statement. "The Palestinian security services have begun searching to find him."
The Spanish consulate in east Jerusalem said it was also working on securing Morenatti's release.
"We're aware of it. We're doing everything we can," a consulate official told AFP.
The last Westerner kidnapping in Gaza occurred in August, when two journalists working for the US-based Fox News television network spent 13 days in captivity after being kidnapped by a previously unknown group, the Holy Jihad Brigades.
The pair, American Steve Centanni and his freelance cameraman, New Zealander Olaf Wiig, were released on August 27.

Copyright AFP (Agence France-Presse), 2006