By William James

JERUSALEM (Reuters) - British Prime Minister David Cameron denounced Iran's government as a "despotic regime" in a speech to Israel's parliament on Wednesday and accused Tehran of making "despicable" efforts to arm Palestinian militants.

His address to the Knesset was staunchly pro-Israeli, and he delighted his hosts by claiming Jewish ancestral roots and talking tough on Iran, which is in negotiations with world powers on curbing its contested nuclear ambitions.

"I share your deep skepticism and great concern about Iran," Cameron said. "I am not starry eyed about the new regime," he added, referring to the election last year of President Hassan Rouhani, seen as a relative moderate in Iran.

The Conservative British leader, on his first visit to Israel since taking power in 2010, also used his speech to throw his support behind U.S. efforts to clinch an elusive Israeli-Palestinian peace deal.

However, he said global tensions around Iran over what Israel and the West fear is its pursuit of nuclear weapons, were likely to persist even if the generations-old Middle East conflict was resolved. Iran denies seeking atomic arms.

"Israel is not the cause of the shadow that Iran casts over the world," Cameron said.

"There is no rule that says if Israel and the Palestinians make peace, Iran is somehow going to dismantle its despotic regime or abandon its nuclear intentions."

Cameron said he had not come to lecture Israel on how to secure peace, and he made only a passing reference to continued Jewish settlement in occupied land that Palestinians say is stifling their aspirations for an independent state.

"We all yearn for a lasting and secure peace between Israel and its neighbors," Cameron said. ‬"We back the compromises needed, including the halt to settlement activity and an end to Palestinian incitement too.‬"

CAPTURED ROCKETS

Britain has strengthened its diplomatic ties with Tehran, appointing a non-resident charge d'affaires in November, but Cameron had harsh words for Iran over Israel's seizure in the Red Sea last week of a ship with rockets hidden in its cargo.

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Israel said the Syrian-made missiles had been supplied by Iran and were intended for Palestinian militants in the Gaza Strip. Iran has denied the accusations.

Cameron said it was "yet another despicable attempt by the Iranians to smuggle more long-range rockets into Gaza".

Soon after the speech - in which Cameron decried "the poisonous ideology of Islamist extremism" - Israeli Army Radio reported that a barrage of missiles were fired at Israel from the Gaza Strip, an enclave ruled by Hamas Islamists.

He also pointed to any future nuclear-armed Iran as "a threat to the whole world" and pledged that Britain would never allow that to happen.

Israeli Prime Minister Benjamin Netanyahu has denounced an interim nuclear deal signed last November by leading powers, including Britain, that allowed an easing of some sanctions against Iran.

He has also repeatedly condemned the possibility that a future accord, already under discussion, might allow Iran to retain some technologies that have bomb-making potential.

Cameron is due to spend just two days in the region and hold separate talks with Netanyahu and Palestinian President Mahmoud Abbas, who are at odds over U.S. proposals to keep peace talks going beyond an April target date for an agreement.

A succession of European leaders have visited Israel in recent months, and just like those before him, Cameron said he would seek to encourage Netanyahu and Abbas to back a framework deal being formulated by U.S. Secretary of State John Kerry.

(Editing by Crispian Balmer)