By Adam Entous

JERUSALEM, July 14 (Reuters) - Israel is considering a plan under which it would stop hunting many Fatah militants and give Palestinians more control over West Bank enclaves to bolster President Mahmoud Abbas, officials and diplomats said Saturday.

Israeli Prime Minister Ehud Olmert's office had no immediate comment on the proposal, but a government official familiar with the deliberations said: "This is something we're considering."

Olmert is expected to meet with Abbas, who leads the secular Fatah faction, on Monday.

Salam Fayyad, whom Abbas appointed prime minister after he dismissed a Hamas-led cabinet last month, has pledged to crack down on militants in the occupied West Bank but said success hinged on Israel agreeing to stop pursuing the gunmen.

Palestinian security forces, dominated by Fatah, have been pursuing Hamas militants in the West Bank since Hamas's violent takeover of the Gaza Strip a month ago. Officials said the goal was to prevent Hamas from building up its West Bank forces.

Abbas swore in three new ministers and reappointed Fayyad as prime minister on Friday, a move Fatah said bolstered the government's legitimacy.

But Hamas, which won parliamentary elections in January 2006, said Fayyad's caretaker government was illegal. "(It) is not constitutional and Hamas will not deal with it in any way or form," Hamas spokesman Fawzi Barhoum said.

Western diplomats briefed on the security proposal under Israeli consideration said it called on Israel to suspend offensive operations in the West Bank targeting dozens of Fatah militants on condition that Abbas's forces ensure that they refrain from attacks against Israeli targets.

The diplomats said the proposal also called for Israel to give Abbas's forces greater security control over Palestinian population centres. Abbas has asked Israel allow the so-called Badr Brigade, a Fatah force based in Jordan, to enter into the West Bank to help bolster security.

Under this proposal, Israel would not halt operations targeting members of Islamic Jihad and Hamas.

Israel's security establishment has resisted similar plans in the past, arguing troops need the freedom to pursue militants, including members of Fatah's al-Aqsa Martyrs Brigades, to prevent attacks on Israelis.

Israel wants to isolate Hamas in the Gaza Strip while allowing funds and goods to flow to Abbas and Fayyad's government in the West Bank.

Olmert has so far balked at removing major West Bank checkpoints and roadblocks to help Abbas's administration, but is handing over in stages hundreds of millions of dollars in frozen tax funds and has agreed to free 250 Fatah prisoners.

U.S. Secretary of State Condoleezza Rice had been expected next week to visit the region for talks with Abbas and Olmert but the trip was postponed.

Rice last visited Israel and the West Bank in March, when she announced that Olmert and Abbas planned to meet every two weeks -- a schedule the two leaders have failed to meet. (Additional reporting by Ori Lewis in Jerusalem and Nidal al-Mughrabi in Gaza)

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