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JERUSALEM, Aug 1 (Reuters) - Israeli Prime Minister Ehud Olmert told U.S. Secretary of State Condoleezza Rice on Wednesday that Hamas Islamists had to be "kept out of the game" while Israel explores new cooperation with the Palestinians.

At their first meeting since Hamas seized control in Gaza, Olmert discussed with Rice the possibility of handing over some security control in the occupied West Bank to President Mahmoud Abbas's forces and said this could only happen "after proper security guarantees" were given, an Israeli spokesman said.

Rice met Olmert during a tour of the region that is aimed at injecting momentum into peace talks between Israel and Abbas's Western-backed government. Abbas dismissed a Hamas-led government after the Islamist group routed his Fatah forces and took over the Gaza Strip last month.

"(Olmert and Rice) spoke about future security cooperation with the Palestinians and Israel's concerns ... about transferring security control of various cities and areas, including Israel's condition that it only happen after proper security guarantees have been given," said Israeli government spokesman David Baker.

Baker said Israel wanted guarantees that "terror will not emerge in those areas again".

"Those security concerns have not yet been satisfied," he said.

Olmert also spoke with Rice about removing roadblocks to improve the freedom of movement for Palestinians in the West Bank, Baker said.

Israeli Defence Minister Ehud Barak, who met Rice earlier on Wednesday, said in statement: "There is a need to build a political horizon with the Palestinians and a need to make their everyday lives easier, though our priority and concern is the security of Israeli citizens."

Rice will meet Abbas on Thursday in the West Bank city of Ramallah.

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