WASHINGTON, April 29 (Arshad Mohammed - Reuters) - Arab states should offer more moral and financial support to Palestinians, reach out to Israelis and stop arming militants to foster Middle East peace, US Secretary of State Hillary Clinton said on Thursday.

In her third speech on the Israeli-Palestinian conflict in two months, Clinton stressed US support for Israel after a period of acute US-Israeli tension while laying out actions she expects of Israel, the Palestinians and Arab countries.

US President Barack Obama's efforts to revive peace talks have been stymied by a disagreement over Jewish settlement construction that has strained ties between Washington and its close ally Israel and by divisions among the Palestinians.

Obama has taken a much tougher line toward Israel than his recent predecessors. Two weeks ago, he described solving the conflict as a vital national security interest, suggesting he may be willing to push both sides hard for a solution.

Clinton's speech appeared designed to quell any lingering anxiety in the American Jewish community about Obama's support for Israel and to make the case for why peace is necessary for the two parties and the broader region.

Arab states ... have an interest in a stable and secure region and they should take specific steps that show Israelis, Palestinians and their own people that peace is possible and that there will be tangible benefits if it is achieved, Clinton said in a speech to the American Jewish Committee.

'BUILD TRUST'
We would hope to see such concrete steps like the opening or reopening of commercial trade offices and interest sections, overflight rights, postal routes, and more people-to-people exchanges that build trust at the grassroots level, she said.

Clinton also urged Arab states to give Palestinian President Mahmoud Abbas greater moral support to negotiate with Israel and more financial backing to help Prime Minister Salam Fayyad build functioning Palestinian institutions.

The US effort to rekindle indirect talks fell apart in March when an Israeli settlement-building announcement angered US officials, who said it was insulting that the decision was unveiled while Vice President Joe Biden was visiting Israel.

Clinton repeated US accusations that Syria has transferred arms to Hezbollah, the political and militant group that controls parts of southern Lebanon, and said Syrian President Bashar al-Assad was making decisions that could mean war or peace for the region.

In what appeared to be a reference to Iran, Clinton also said that no state should arm Hamas, the Palestinian group that controls the Gaza Strip.

Speaking after Clinton, Israeli Defense Minister Ehud Barak said Israel sees heavy clouds looming over the horizon: Hamas in the south, Hezbollah in the north and, of course, Iran.

The United States and some of its allies, including Israel, accuse Iran of seeking to develop nuclear weapons. Iran denies this, saying its nuclear program is to generate power.

Clinton said the United States is trying to give Iran a choice of reining in its nuclear program and benefiting from normal relations or increased isolation and painful consequences.

At every turn, Iran has met our outstretched hand with a clenched fist, she said, but added that the US effort to engage Iran had made it easier to persuade other countries to consider a fourth UN Security Council sanctions resolution on Tehran.