Israeli Prime Minister Benjamin Netanyahu attends a weekly cabinet meeting in Jerusalem Thomson Reuters MUNICH (Reuters) - Saudi Arabia and Israel both called on Sunday for a new push against Iran, signaling a growing alignment in their interests, while U.S. lawmakers promised to seek new sanctions on the Shi'ite Muslim power.

Turkey also joined the de facto united front against Tehran as Saudi and Israeli ministers rejected an appeal from Iranian Foreign Minister Mohammad Javad Zarif for Sunni Gulf Arab states to work with Tehran to reduce violence across the region.

While Saudi Arabia remains historically at odds with Israel, their ministers demanded at the Munich Security Conference that Tehran be punished for propping up the Syrian government, developing ballistic missiles and funding separatists in Yemen.

International sanctions on Iran were lifted a year ago under a nuclear deal with world powers, but Republican senators said at the conference they would press for new U.S. measures over the missiles issue and Tehran's actions to "destabilize" the Middle East.

Saudi Foreign Minister Adel al-Jubeir called Tehran the main sponsor of global terrorism and a destabilizing force in the Middle East.

He sidestepped a question about Israel's call for concerted action with Sunni Arab states amid growing speculation that the two countries could normalize relations and join forces to oppose Tehran, much as Turkey has done.

The six Arab members of the Gulf Cooperation Council (GCC), especially Saudi Arabia, accuse Iran of using sectarianism to interfere in Arab countries and build its own sphere of influence in the Middle East. Iran denies the accusations.

"Iran remains the single main sponsor of terrorism in the world," Adel al-Jubeir told delegates at the conference. "It's determined to upend the order in the Middle East ... (and) until and unless Iran changes its behavior it would be very difficult to deal with a country like this."

Saudi Foreign Minister Adel Al-Jubeir speaks during a joint news conference with his Jordanian counterpart Nasser Judeh at the Ministry of Foreign Affairs in Amman, Jordan, July 9, 2015. Majed Jaber/Reuters Al-Jubeir said Iran was propping up the government of President Bashar al-Assad in the Syrian civil war, funding the Houthi movement in Yemen and fomenting violence across the region.

The international community needed to set clear "red lines" to halt Iran's actions, he said, calling for banking, travel and trade restrictions aimed at changing Tehran's behavior.

Israeli Defence Minister Avigdor Lieberman said Iran's ultimate objective was to undermine Riyadh, and called for a dialogue with Sunni Arab countries to defeat "radical" elements in the region.

"The real division is not Jews, Muslims ... but moderate people versus radical people," Lieberman told delegates.

Turkish Foreign Minister Mevlut Cavusoglu also criticized what he called an Iranian "sectarian policy" aimed at undermining Bahrain and Saudi Arabia.

"Turkey is very much against any kind of division, religious or sectarian," he said. "It's good that we are now normalizing our relations with Israel."

Zarif opened Sunday's session with the call for dialogue to address "anxieties" in the region. This followed a visit by Iranian President Hassan Rouhani to Oman and Kuwait last week to try to improve ties, his first visit to the Gulf states since taking power in 2013.

Iranian Foreign Minister Mohammad Javad Zarif speaks to the media after closed-door nuclear talks on Iran take place in Vienna, Austria, Tuesday, July 15, 2014. AP Asked if Iran's envisioned regional dialogue could include Israel, Zarif said Tehran was looking at a more "modest" approach. "I'm focusing on the Persian Gulf. We have enough problems in this region so we want to start a dialogue with countries we call brothers in Islam," he said.

Zarif dismissed any suggestions his country would ever seek to develop nuclear weapons. When asked about the new U.S. administration's tough rhetoric on Iran's role in the region and calls to review the nuclear deal, he said Tehran did not respond well to threats or sanctions.

U.S. Senator Lindsey Graham, a South Carolina Republican, said he and other senators were preparing legislation to further sanction Iran for violating U.N. Security Council resolutions with its missile development program and other actions.

"It is now time for the Congress to take Iran on directly in terms of what they’ve done outside the nuclear program," he said.

Senator Christopher Murphy, a Democrat and member of the Senate Foreign Relations Committee, said Washington needed to decide whether to take a broader role in the regional conflict.

"We have to make a decision whether we are going to get involved in the emerging proxy war in a bigger way than we are today, between Iran and Saudi Arabia," he said.

(Additional reporting by Vladimir Soldatkin; editing by David Stamp)