DUBAI, May 4 (Reuters) - The United States would support a Turkish-brokered Syrian-Israeli peace drive but wants to see Damascus change its policy on Lebanon, U.S. Secretary of State Condoleezza Rice said in remarks published on Sunday.

"We do not wish to stand in the way of any attempt to achieve peace between Israel and its neighbours including Syria," Rice told Asharq al-Awsat newspaper in remarks translated into Arabic.

"If the two sides wished to exert an effort for peace the United States would give its blessing and back these efforts. The problem is that Syria is yet to show a desire for Middle East peace especially vis-a-vis Lebanon," she added.

Syria says it received word from Turkey that Israel was willing to give back the occupied Golan Heights in full in return for peace with the Arab state -- one of the main issues that led decade-long negotiations to falter in 2000.

Syrian President Bashar al-Assad has said Syria was ready to negotiate with Israel through Turkey to "find common ground" for peace, but any direct talks must wait until a new U.S. president is elected.

U.S. President George W. Bush's administration has been cool to renewing Israeli-Syrian negotiations, which collapsed in 2000 without resolving the fate of the Golan Heights, Syrian and Israeli officials say.

Washington accuses Syria of meddling in Lebanon, where Damascus had the final say in politics for almost three decades until 2005 when it ended 29 years of military presence following the murder of former Lebanese Prime Minister Rafik al-Hariri.

"What should not happen is that we talk to Syria about peace ignoring Lebanon," Rice said. "The Syrians should demarcate their border with Lebanon ... and send an ambassador to Lebanon and stop dealing with it as a Syrian district."

Rice also said that talking about peace with the Syrians should not eclipse a U.S. drive to push for an Israeli-Palestinian peace deal.

Rice also made a swipe at Iran, an ally of Syria, which it also accuses of meddling in Beirut's politics through guerrilla group Hizbollah. "Iran is behind all problems in the region."

Syrian-Israeli talks collapsed in 2000 over the scope of an Israeli pullout from the Golan Heights, occupied since 1967. (Reporting by Inal Ersan; editing by Sami Aboudi)

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