By Brenda Gazzar

JERUSALEM, Jan 2 (Reuters) - Defence Minister Ehud Barak said on Wednesday Israel would watch closely whether the Palestinian Authority fulfilled a promise to prosecute two suspects in the killing of two off-duty Israeli soldiers.

"These people need to rot in jail until their last days," Barak told Israel Radio.

"We will see if the Palestinian Authority is opening a revolving door for them and if so, the Israeli Defence Forces and security services will know how to put our hands on them," he said.

The ambush that killed the two soldiers in the occupied West Bank on Friday has raised questions in Israel over the effectiveness of a pledged security crackdown against militants by forces loyal to Palestinian President Mahmoud Abbas.

Israel has made implementation of any peace deal it reaches with the Palestinians following the U.S.-hosted Annapolis summit in November conditional on reining in militants. U.S. President George W. Bush is to visit Israel and the West Bank next week.

The Palestinians argue Israel has failed to meet its own obligations to freeze settlement activity under a U.S.-backed peace "road map" agreed in 2003.

The two armed soldiers, settlers who lived near the city of Hebron, killed two of their attackers before succumbing to their wounds.

Palestinian security forces in Hebron arrested the two surviving gunmen the day after the attack, a Palestinian security official said.

Palestinian Information Minister Riyad al-Malki said that if found guilty, the men would pay for their crimes in the West Bank.

"The investigation is still going on. They will be tried and once there is a verdict they will stay in prison until they finish their sentence," said Malki, who also serves as foreign minister.

Israel has argued in the past that the Palestinians have paid lip service to security, quickly freeing militants from jail in what it has termed a "revolving door" policy.

Abbas's government has deployed hundreds of security men in chaotic West Bank towns as part of a Western-backed crackdown on gangsters and militants, and are at pains to prove they are exerting control in the territory following the takeover of the Gaza Strip by Hamas Islamists in June. (Additional reporting by Mohammed Assadi in Ramallah and Ari Rabinovitch in Jerusalem; Writing by Rebecca Harrison; Editing by Matthew Tostevin)

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