Edelstein was speaking to a meeting of the "Friends of Israel Initiative" in the Knesset when he noted the Palestinians had agreed not to take any unilateral steps towards international recognition during the nine months of negotiations which Secretary of State John Kerry restarted in July 2013.
Prime Minister Benjamin Netanyahu "was prepared to move forward, but the Palestinians made their position clear yesterday," Edelstein said to the attendees.
He told them that Israel had been "prepared to pay a very heavy price; and not everyone was sure this was the right – to pay the price of the release of terrorists."
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Foreign Minister Avigdor Lieberman echoed the sentiment, saying Israel had done "all it could to try and reach a settlement with the Palestinians, and now the ball is in their court."
Minister of Housing and Construction Uri Ariel, on the other hand, reserved harsh criticism for the unilateral Palestinian moves. He said Abbas "ran to the UN and effectively announced the cancellation of the Oslo Accords."
He expressed his belief that "Israel should use this opportunity – announce an end to these damned agreements, to enforce its complete jurisdiction in all the territories, and to give Arabs the same civil status that Arabs from East Jerusalem have received."
'Disgrace to Israel'
Justice Minister and chief Israeli peace negotiator Tzipi Livni, however, chose a more diplomatic approach, reminding the Palestinian leadership that unilateral moves are not in their best interest.
"The treaties filed by the Palestinians at the UN are not encouraging, but we can't throw in the towel. The Palestinians' move harms the interests of the Palestinians," she said.
She emphasized: "If they want a state, they need to understand it must come through the peace process."
Livni met Wednesday night with chief Palestinian negotiator Saeb Erekat and US envoy to the talks Martin Indyk in an attempt to salvage the faltering talks.
Meanwhile Deputy Foreign Minister Ze'ev Elkin sharply criticized Livni's meeting with Erekat. He said "holding this meeting, after the Palestinians' turn to the UN against all of their commitments, is disgraceful to the State of Israel."
Elkin called on "the prime minister and the justice minister to halt the negotiations until (Abbas) reconsidered his applications to the UN."
Moran Azulay contributed to this report.