* U.S. concerned about support for "terrorist" groups

* Peace between Syria and Israel remains a key goal

By Susan Cornwell

WASHINGTON, Oct 28 (Reuters) - The United States wants to move beyond dialogue to a more constructive relationship with Syria but will not trade away Lebanon's sovereignty to do so, a senior State Department official said on Wednesday.

Jeffrey Feltman, Assistant Secretary of State for Near Eastern affairs, said while recent trips to Syria by himself and U.S. special envoy George Mitchell had laid the groundwork, "we believe that there is further potential for a positive, constructive U.S.-Syrian relationship."

But for its potential to be realized, Syria must address U.S. concerns about some of its regional policies, such as its support for "terrorist" organizations like the Lebanese movement Hezbollah and the Palestinian group Hamas and its control of foreign fighters trying to enter Iraq, Feltman told U.S. lawmakers.

"Our dialogue with the Syrians is not going to come at the expense of Lebanon's sovereignty," he added in testimony to a House Foreign Affairs subcommittee.

Feltman said that in Lebanon, there were expectations that a cabinet could be announced in the coming days, and "we certainly hope this is the case." He did not elaborate.

Lebanon held a parliamentary election in June, when voters endorsed the U.S.-backed anti-Syrian coalition led by Saad Al-Hariri, son of assassinated statesman Rafik al-Hariri. But the failure to form a new government since then has underlined the potential for setbacks in its fragile politics.

Syria dominated Lebanon until the killing of Rafik al-Hariri in 2005, which led to the withdrawal of its troops from the country. Damascus still holds great sway through allies such as Hezbollah, a heavily armed Lebanese Shi'ite group which also has strong Iranian backing.

The administration of U.S. President Barack Obama started talks with Syria soon after he was inaugurated in January, ending a boycott of several years under his predecessor George W. Bush.

During a trip to Syria in May, Feltman told the Syrian government the United States was committed to seeking a peace deal between Syria and Israel, a main objective for Damascus in its rapprochement with Washington. (Editing by Eric Walsh)

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