Interim Iraqi Prime Minister Iyad Allawi shook hands with Israeli Foreign Minister Silvan Shalom on Tuesday at the UN General Assembly, where alphabetical order put them side by side.
"[It] is a sign of one of the most dangerous goals of the American war on Iraq, yanking Iraq from its place in the Arab and Muslim worlds and sticking it in the US-Zionist political cosmos," Hizb Allah said in a statement on Thursday.
"This unacceptable handshake is at once a true insult to the Iraqi people, their history, culture and Islamic and national commitment; and flagrant scorn for the suffering of Palestinian people and the sentiments of Arabs and Muslims," it said.
Shalom said the incident was the first official contact between Israel and Baghdad since the US invasion of Iraq, which Israel attacked in 1981 saying it was to destroy a nuclear reactor.
Iraq fired missiles at Israel during the 1991 Gulf war when Saddam Hussein answered demands to pull his army out of Kuwait by saying Israel must in turn end its occupation of the West Bank and Gaza Strip.