Shimon Peres, the deputy prime minister, said: "Saddam Hussein brought about his own demise. This was a man who caused a great deal of harm to his people and who was a major threat to Israel."
However, the ruling Palestinian movement, Hamas, described the execution as a "political assassination" which "violates all international laws".
The oppostion Palestinian Fatah faction said that the execution was "a disrespectful tribute to Eid al-Adha, and should never have taken place now".
Libya declared three days of national mourning and described Saddam as a "prisoner of war".
Saudi Arabia also expressed its "surprise and dismay" at the execution.
The Saudi Press Agency, which expresses the official line, also criticised the "politicisation" of Saddam's trial.
Held to account