JERUSALEM (Reuters) - Israel's cabinet on Sunday approved the release of 104 Arab prisoners to help restart U.S.-brokered peace talks with the Palestinians after nearly three years of diplomatic stagnation.

Thirteen ministers in Prime Minister Benjamin Netanyahu's coalition cabinet voted in favor of the prisoner release, seven voted against and two abstained, a government official said.

"The cabinet has authorized the opening of diplomatic talks between Israel and the Palestinians...," said a statement issued by the prime minister's office.

Netanyahu had urged divided rightists in his cabinet to back the prisoner deal.

"This moment is not easy for me, is not easy for the cabinet ministers, and is not easy especially for the bereaved families, whose feelings I understand," he said when the cabinet met, referring to families who have lost members in militant attacks.

"But there are moments in which tough decisions must be made for the good of the nation and this is one of those moments."

Justice Minister Tzipi Livni, who is set to head Israel's negotiation team, told her cabinet colleagues that resuming talks with the Palestinians was a vital national interest.

"Today's cabinet decision is one of the most important for the future of Israel... Starting a (peace) process is in Israel's security and strategic interests," Livni said.

Palestinian President Mahmoud Abbas has demanded the release of prisoners held since before a 1993 interim peace accord took effect. Israel has jailed thousands more Palestinians since then, many for carrying out deadly attacks.

The prisoner release would allow Netanyahu to sidestep other Palestinian demands, such as a halt to Jewish settlement expansion and a guarantee that negotiations over borders will be based on boundaries from before the 1967 Middle East war, when Israel captured the West Bank, Gaza Stripand East Jerusalem.

Chief Palestinian negotiator Saeb Erekat welcomed Israel's decision, which he said had come 14 years late, and pledged to work for the release of all prisoners held by Israel.

"This Israeli cabinet decision is an overdue step towards the implementation of the Sharm el-Sheikh agreement of 1999," he said in a statement. "We call on Israel to seize the opportunity ... to put an end to decades of occupation and exile and to start a new stage of justice, freedom and peace for Israel, Palestine and the rest of the region."

In any future peace deal, Israel wants to keep several settlement blocs and East Jerusalem, which it annexed as part of its capital in a move never recognized internationally.

Hundreds of protesters from the Popular Front for the Liberation of Palestine (PFLP) staged a rally against the resumption of peace talks, clashing with police in the West Bank city of Ramallah, the seat of Abbas's Palestinian Authority.

PFLP activists also demonstrated in Gaza and chanted: "Listen Abbas, our land is not for sale... The (Palestinian) cause will never be resolved except by the rifle."

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Appealing for support on his Facebook page on Saturday, Netanyahu said the inmates would be freed in groups only after the start of talks, expected to last at least nine months.

The 22-member cabinet also discussed legislation that would require a referendum on any statehood deal reached with the Palestinians involving a withdrawal from land Israel captured in the 1967 war. It will be sent for parliamentary debate shortly.

The U.S.-sponsored talks, expected to reconvene in Washington as early as Tuesday, broke down in late 2010 in a dispute over Israeli settlement construction in the West Bank, which Palestinians say denies them a viable state.

Before the cabinet meeting, Netanyahu told ministers from his Likud party that Israel would pay a price if peace talks did not resume, according to one official who was there.

The latest diplomatic push follows months of intense shuttle diplomacy by U.S. Secretary of State John Kerry who said a week ago the groundwork had been laid for a breakthrough, while setting no specific date for talks to restart.

(Additional reporting by Allyn Fisher-Ilan and Ari Rabinovitch in Jerusalem, Ali Sawafta in Ramallahand Nidal al-Mughrabi in Gaza; Editing by Alistair Lyon)