WASHINGTON, Apr. 17 (Reuters) - The U.S. and its allies planned fresh sanctions against Iran over its unprecedented attack on Israel, seeking to dissuade Israel from a major escalation as its war cabinet was set to meet for a third time on Wednesday to decide a response.

While Saturday night's attack caused no deaths and little damage thanks to the air defences and countermeasures of Israel and its allies, it has increased fears that violence rooted in the six-month-old Gaza war is spreading, with the risk of open war between long-time adversaries Iran and Israel.

Israel's military chief of staff Herzi Halevi had promised Iran's launch of more than 300 missiles, cruise missiles and drones at Israeli territory "will be met with a response", but gave no details.

An Israeli government source said the war cabinet session scheduled for Tuesday had been put off until Wednesday, without elaborating.

Hoping to steer Israel away from massive retaliation, the U.S. and Europe flagged a toughening of economic and political sanctions against Iran.

The U.S. is planning to impose new sanctions targeting Iran's missile and drone programme in the coming days and expects its allies will be following suit, National Security Advisor Jake Sullivan said in a statement on Tuesday.

Earlier, Treasury Secretary Janet Yellen said the U.S. would use sanctions, and work with allies, to keep disrupting Iran's "malign and destabilising activity".

She told a news conference in Washington all options to disrupt Iran's "terrorist financing" were on the table, and she expected further sanctions against Iran to be announced soon.

European Union foreign policy chief Josep Borrell, speaking in Brussels after an emergency video conference of EU foreign ministers, said some member states had asked for sanctions against Iran to be expanded and that the bloc's diplomatic service would begin working on the proposal.

Borrell said the proposal would expand a sanctions regime that seeks to curb the supply of Iranian drones to Russia so that it would also include the provision of missiles and could also cover deliveries to Iranian proxies in the Middle East.

Israeli Foreign Minister Israel Katz said he was "leading a diplomatic attack", writing to 32 countries to ask them to place sanctions on Iran's missile programme and follow Washington in proscribing its dominant military force, the Revolutionary Guard Corps, as a terrorist group.

Photo from Reuters