JERUSALEM, June 15 (Reuters) - U.S. Secretary of State Condoleezza Rice said on Sunday it was "extremely important" Israel allow three Palestinians to leave the Hamas-controlled Gaza Strip to take up prestigious U.S. fellowships.

Earlier this year the U.S. government was embarrassed when it became public it had withdrawn Fulbright fellowships for seven Gaza students because Israel had not granted them exit permits from the blockaded territory.

Israel tightened its cordon of the Gaza Strip after the Hamas Islamist group took control there nearly a year ago. Israel gives few Palestinians, other than some who are gravely ill, permission to leave.

Israel has also tightened rules for Palestinian staff of the United Nations who travel in and out of the occupied West Bank, internal U.N. emails and aid workers say.

After media reports about the students' case, the United States restored the fellowships and formally asked Israel to allow them to leave Gaza.

Israel subsequently allowed four of seven Palestinians to leave Gaza to apply for U.S. visas but the other three have not received permission to leave for visa interviews at the U.S. consulate in Jerusalem, Sari Bashi, the head of the Israeli human rights group Gisha, said.

Earlier this month, the Israeli Supreme Court criticised the government for preventing the students from leaving Gaza and gave it two weeks to review its policy.

"I consider it extremely important for these young people to be able to take up their fellowships," Rice told U.S. reporters.

"Unless there is something that I have not yet seen -- and I don't rule out that there may be some reason that we have not yet seen -- but unless I see some other reason ... we are going to continue to work to try to get them help," she added.

"I consider it to be a very high priority to get this resolved," she said.

An Israeli official who coordinates civilian affairs between Israel and Gaza said security concerns were the reason for the refusal to travel.

"The three were denied permits to travel because of specific security concerns and is the reason they were not allowed out (of Gaza)," the official, Peter Lerner, said.

Gisha said Israel was preventing hundreds of students from leaving Gaza to go to foreign universities at which they have been accepted for studies.

"Since January 2008, Israel has refused to let young people in Gaza study abroad," Gisha said in a statement. (Additional reporting by Ori Lewis; Writing by Arshad Mohammed; Editing by Matthew Jones)

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