George Mitchell, right, will shuttle between the two sides
Indirect peace talks between Israel and the Palestinians are finally under way after months of political deadlock.
The first round of talks ended with the US confirming its envoy George Mitchell would return to the region next week.
The US urged both sides to keep up the effort after Mr Mitchell met Palestinian Authority President Mahmoud Abbas on Sunday.
Mr Mitchell will now shuttle between the two sides, with hopes that direct talks can start within four months.
The United States warned both sides not to undermine the peace effort - or be held "accountable".
'We will respond'
The start of indirect talks in March was halted by a row over the building of 1,600 new Israeli homes in occupied East Jerusalem.
The White House said Israel had agreed that no building would take place at the site, Ramat Shlomo, for two years.
Israeli officials denied that any commitments had been given, but said that under normal planning procedures it would be several years before construction would start anyway.
Palestinians broke off direct peace talks after Israel launched a military offensive on Gaza in late 2008.
Tim Franks, BBC News, Jerusalem
The air is thick with mutual mistrust at the prospect of negotiations.
There are many Israelis who believe that the Palestinians are not sincere about talks, that the Palestinian leadership simply wants the Americans to impose a solution which meets its desires.
They also point out that the land earmarked for a Palestinian state remains politically divided between the West Bank and the Gaza Strip, from where the Islamist Hamas movement is deeply hostile to this peace process.
The Palestinians, for their part, believe that this right-wing Israeli government is far from committed to the idea of a Palestinian state, and simply wants negotiations which meander on pointlessly for years.
One diplomat close to the process said that expectations were at "zero" for now. The fact that after nearly 20 years of on-off negotiations, all that was now being offered was indirect talks through the US special envoy was, he said, "a badge of how far the Americans have mismanaged the situation".
"The proximity talks have started," the Palestinian chief negotiator, Saeb Erekat, said on Sunday, after Mr Mitchell met Palestinian President Mahmoud Abbas.
He spoke in the West Bank city of Ramallah, with Mr Mitchell standing beside him.
US State Department spokesman Philip Crowley gave his warning in a statement after the talks.
He said: "As both parties know, if either takes significant actions during the proximity talks that we judge would seriously undermine trust, we will respond to hold them accountable and ensure that negotiations continue."
But he said talks the Mr Mitchell held with both sides in the past week were "serious and wide-ranging".
Mr Mitchell will now shuttle between the Israeli and Palestinian leaders to try to narrow their differences on the terms of Palestinian statehood.
Mr Netanyahu said on Sunday that he hoped the indirect talks would quickly move to direct negotiations.
"Peace cannot be brought about from a distance, or with a remote control," he told a meeting of the Israeli cabinet.
"We are neighbours of the Palestinians and they are our neighbours. Over time one cannot assume that that we will reach decisions and agreements on critical issues such as security and our national interests and their interests if we don't sit in the same room."
The talks went ahead a day after receiving the backing of the Palestine Liberation Organisation (PLO).
However, the Palestinian Islamist group, Hamas, which controls the Gaza Strip, had urged the PLO to reject the talks, warning it not to "give cover to the Israeli occupation to commit more crimes against our people".
On Sunday night, the Israeli military said it had bombed two "terrorist sites" in the south of the Gaza Strip, in response to a rocket fired at the Ashkelon area of southern Israel on Saturday.
Hamas security forces said a missile had hit a smuggling tunnel, causing damage but no casualties, AFP news agency reported.
Correspondents say the launch of the proximity talks marks the first concrete achievement in the Obama administration's Middle East peace efforts.
Palestinians pulled out of talks in March after Israeli municipal authorities approved plans for 1,600 new homes in the East Jerusalem settlement of Ramat Shlomo.
The announcement was made during a visit to Israel by US Vice-President Joe Biden and caused great strain in Israeli-US relations.
The Palestinian Authority's formal position is that it will not enter direct talks unless Israel completely halts building in the West Bank and East Jerusalem.
In November, Israel announced a 10-month suspension of new building in the West Bank, under intense US pressure.
But it considers areas within the Jerusalem municipality as its territory and thus not subject to the restrictions.
Israel has occupied the West Bank, including East Jerusalem, since 1967. It insists Jerusalem will remain its undivided capital, although Palestinians want to establish their capital in the east of the city.
Nearly half a million Jews live in more than 100 settlements in the West Bank, among a Palestinian population of about 2.5 million.
The settlements are illegal under international law, although Israel disputes this.