JERUSALEM, June 12 (Reuters) - Israeli Prime Minister Ehud Olmert has relayed a new message to Syria about the possibility of renewing peace talks between the two countries, an Israeli newspaper reported on Tuesday.

The report carried by the Haaretz daily came after Israeli officials confirmed in the past few days that the Jewish state was using secret channels to test whether talks that stalled in 2000 could proceed anew.

Olmert had relayed comments containing "interesting nuances" to Greek Foreign Minister Dora Bakoyannis on Monday before she headed to Damascus, the newspaper quoted an unidentified Israeli political source as saying.

The newspaper gave no further details about the message.

Olmert has made clear in past messages Israel was willing to withdraw from the Golan Heights, captured by the Jewish state in a 1967 war, but has demanded in return that Syria cut ties with Iran, Hezbollah and Palestinian militant groups.

Bakoyannis had told Olmert she was seeking to further peace prospects in the Middle East, said Haaretz. But a Greek Foreign Ministry spokesman was quoted as denying Greece was acting as a mediator in the region.

Olmert's spokesmen could not be reached immediately for comment.

On Saturday, Israeli Deputy Prime Minister Shaul Mofaz said on Israel Radio "we have turned to Syria with secret channels" but there had not yet been any Syrian response.

Syrian President Bashar al-Assad has expressed interest in resuming talks with Israel that stalled over the terms for a peace deal, but has also hinted Syria could resort to force if it deemed diplomacy a dead end.

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