JERUSALEM, March 19 (Reuters) - U.S. Republican presidential candidate John McCain told Palestinian President Mahmoud Abbas he was committed to a peace settlement after President George W. Bush leaves office, a Palestinian official said on Wednesday.

At a news conference with Israeli Foreign Minister Tzipi Livni, McCain said he had telephoned Abbas, who is based in the West Bank city of Ramallah just a few kilometres (miles) away, because he was unable to meet the Palestinian president in person.

McCain, visiting Israel as part of what the candidate described as a Middle East fact-finding tour, said the Western-backed leader wants to move forward in peace talks.

"I again believe that President Abbas wants to get this (peace) process started," McCain said in Jerusalem.

McCain said he shared Israel's concern about the deterioration of security in the Gaza Strip and the cross-border rocket fire from the Hamas-controlled territory against Israel.

"I believe that (Abbas) does not support the kind of activity that is taking place in Gaza. I know that the United States government is fully committed to trying to stop this ... cross-border violence," McCain said.

McCain and Senate allies, Democrat-turned-Independent Joe Lieberman of Connecticut and South Carolina Republican Lindsey Graham, planned to meet Israeli Prime Minister Ehud Olmert later on Wednesday.

The 71-year-old ex-aviator and Vietnam war POW has denied seeking to improve his electoral prospects on this tour, saying he came as a top member of the Senate Armed Services Committee rather than as Bush's potential successor. (Additional reporting by Wafa Amr in Ramallah, Writing by Ari Rabinovitch; Editing by Samia Nakhoul)

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