Israel and the Palestinians held last-ditch talks with a U.S. envoy Sunday on salvaging their teetering peace talks, after the Jewish state threatened to take retaliatory measures.

Warning that the peace process was on the edge of collapse, an Israeli official close to the talks said that even U.S. Secretary of State John Kerry, its tireless sponsor, was cooling off.

A rocket fired from the Hamas-ruled Gaza Strip hit an open area in southern Israel late Saturday without causing damage or injuries, the army and police said.

"Another rocket hit Hof Ashkelon," the army said in a statement, while police said it caused no harm or damage.

Israel's chief negotiator called on Saturday for direct talks with the Palestinians, as attempts continue to prevent the collapse of peace negotiations.

Tzipi Livni's remarks came on the eve of a three-way meeting with her Palestinian counterpart Saeb Erakat and U.S. envoy Martin Indyk, officials close to the talks said. Indyk met the two separately Friday.

European foreign ministers on Saturday said they fully supported efforts by U.S. Secretary of State John Kerry to keep Middle East peace talks alive as tension mounted on both sides.

"We support the efforts of Secretary of State Kerry," EU foreign affairs chief Catherine Ashton said at the close of a two-day meeting in Athens.

Israeli and Palestinian negotiators will meet jointly Sunday with U.S. envoy Martin Indyk, as attempts continue to prevent the collapse of peace negotiations, officials close to the talks said.

The first three-way meeting since Wednesday comes as Washington reviews its push for a peace deal after a spiral of tit-for-tat moves by Israel and the Palestinians took hard-won negotiations close to collapse.

The White House Friday defended "tireless" Secretary of State John Kerry, saying his long-odds Middle East peace bid had not been a waste of time because the stakes were so high.

The administration rode to Kerry's defense amid rising criticism of his decision to devote so much time to the peace effort, which appears on the verge of collapse.

Israel has approved a controversial archaeology project in annexed east Jerusalem, the interior ministry said Friday, in a move likely to compound tensions threatening to scupper peace talks with the Palestinians.

The ministry "heard objections" from the Palestinians and from residents to the plans to build a visitor center just outside Jerusalem's Old City walls in the Arab neighborhood of Silwan, a statement said.

Israel is considering retaliatory measures against the Palestinians in response to their renewed drive for international recognition of their promised state, Israeli media reported on Friday.

Prime Minister Benjamin Netanyahu and Defense Minister Moshe Yaalon have asked the head of the Israeli military administration in the occupied West Bank, General Yoav Mordechai, to draw up a range of options, the Haaretz newspaper reported.

Israel has told the Palestinians that a planned release of 26 prisoners cannot proceed, placing already embattled peace talks in further jeopardy after both sides took steps Washington called "unhelpful."

Israel's chief negotiator with the Palestinians has told them that the planned release cannot go ahead, a source close to the embattled talks told Agence France Presse on Thursday.

Israeli Foreign Minister Avigdor Lieberman will fly to the United States Friday for talks including with Secretary of State John Kerry amid a crisis in peace talks with the Palestinians.

Lieberman's office said in a statement on Thursday he would be in New York on Friday to meet Mayor Bill de Blasio and American Jewish leaders.