(Adds Rice, Abbas comments)

By Arshad Mohammed

RAMALLAH, West Bank, March 25 (Reuters) - U.S. Secretary of State Condoleezza Rice set out a new approach on Sunday to reviving Israeli-Palestinian peace efforts, saying she would pursue "parallel" talks with the two parties.

"Now we are in a situation in which I think a bilateral approach, in which I talk in parallel to the parties ... is the best way," Rice said at a news conference with Palestinian President Mahmoud Abbas.

She said she hoped to find a common agenda between both sides, who are deeply divided over the recent establishment of a Palestinian unity government, that would eventually lead to the creation of a Palestinian state.

"You need to prepare the ground well, you need to spend time with the parties. You need to understand what is tolerable (for) each side," Rice said.

The strategy appeared to set the stage for shuttle diplomacy, at least during her current visit.

Rice planned to see Israeli Prime Minister Ehud Olmert later in the day and again on Monday, after returning from Amman and a second round of talks with Abbas, who will be visiting the Jordanian capital.

She has been touring the Middle East, trying to persuade Arab governments to make a peace plan they ratified in 2002 more attractive to Israel by adding what she calls "active diplomacy" -- seen as code for early contacts with Israelis.

After Abbas formed a unity government with Hamas Islamists earlier this month, Olmert signalled that direct talks with the Palestinian president would go nowhere and pledged to limit any future face-to-face meetings to humanitarian issues.

Israel and the Quartet of Middle East negotiators -- the United States, the European Union, the United Nations and Russia -- have demanded the Palestinian government recognise Israel, renounce violence and accept existing interim peace deals.

The unity administration agreed only to "respect" previous accords and stopped short of recognising Israel.

CAPTIVE SOLDIER

Speaking to his cabinet on Sunday, Olmert accused Abbas of reneging on what he said was a promise to secure, before the Palestinian government was inaugurated, the release of an Israeli soldier held by Gaza militants.

"Obviously, all these things will not, in the near future, facilitate contacts between us and the Palestinian Authority," Olmert said in broadcast remarks.

At the news conference with Rice, Abbas said the soldier, Corporal Gilad Shalit, was alive and in good health.

"We have a responsibility to preserve his life ... and that is why a long time has been spent (trying to secure) his release," Abbas said. Palestinians want Israel to free hundreds of their brethren in exchange for the soldier.

Egypt, which Rice visited before flying on to Tel Aviv, said Arab states were ready to negotiate with Israel if the Jewish state accepted the 2002 peace initiative as a starting point.

But Arab states, meeting in Riyadh on March 28 and 29, will not amend their initiative, which Israel says it finds problematic, before Israel makes the first move, Egyptian Foreign Minister Ahmed Aboul Gheit said.

The plan offers Israel normal relations with all Arab states in return for withdrawal from land captured in 1967 and a solution for Palestinian refugees. Israel has repeatedly rejected the proposal but has recently shown some interest. (Additional reporting by Mohammed Assadi in Ramallah, Jeffrey Heller in Jerusalem and Alaa Shahine in Aswan, Egypt)

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