Mr Mitchell (left) and Mr Netanyahu both said they were pushing for peace
US Middle East envoy George Mitchell is meeting Israeli and Palestinian leaders in the hope of ending a row over Israeli building in East Jerusalem.
Mr Mitchell met Israeli PM Benjamin Netanyahu on Friday, on his first visit since the disagreement scuppered planned indirect peace talks.
Reports suggested Israel may be willing to make several gestures to bring the Palestinians back to the negotiations.
But Israel's PM has stressed he will not stop building in East Jerusalem.
Ahead of his meeting with Mr Mitchell, Mr Netanyahu said Israel was "serious" about trying to advance peace, and hoped the Palestinians would "respond".
Mr Mitchell stressed the "unbreakable bond" between the US and Israel.
Officials said the two would meet again on Sunday, after Mr Mitchell has met Palestinian Authority President Mahmoud Abbas later on Friday.
The Palestinians pulled out of the scheduled "proximity talks" last month after Israel approved a plan for 1,600 homes in East Jerusalem, where the Palestinians want the capital of their future state.
That announcement, as US Vice-President Joe Biden was visiting to launch the negotiations, triggered a crisis in relations between Israel and its greatest ally, Washington.
A planned visit by Mr Mitchell in March was cancelled.
The US has requested that Israel make a series of moves, which have not been officially made public, to reassure the Palestinians.
As Mr Mitchell arrived, Mr Netanyahu stressed in a television interview that he would not yield to US pressure to completely halt building in the occupied East of Jerusalem.
"I am saying one thing: there will be no freeze in Jerusalem," he said.
But on Thursday, the Wall Street Journal quoted unnamed US officials as saying that Mr Netanyahu had offered measures including easing the blockade on Gaza, releasing prisoners, freezing the controversial building project in Ramat Shlomo for two years, and agreeing to discuss borders and the status of Jerusalem.
In Washington, a US state department spokesman said there had been "good give and take" with the Israelis.
The decision that Mr Mitchell would visit was only made on Wednesday, with reports from lower level US-Israeli meetings suggesting it would be "fruitful for him to travel", the spokesman, PJ Crowley. said.
But he added that the Israelis still had not done everything the US wanted.
"The status quo is not sustainable," he warned.
Palestinian chief negotiator Saeb Erekat said the Palestinians "should give the proximity talks the chance they deserve".
But he added: "It is evident after Mr Netanyahu's statements that this Israeli government is determined to continue the course of settlements, dictation and confrontation and not peace and reconciliation."
The Palestinians' position on exactly what Israel must do before they would join indirect talks remains unclear.
Since the row broke out, Mr Abbas has said Israel must halt all settlement activity, including in East Jerusalem, though he initially agreed to the negotiations without a total freeze.
But a senior Palestinian official has told the BBC the Ramat Shlomo project must be put on ice for at least three years, and the Israelis must not "continue to take actions which destroy our credibility".
Mr Netanyahu has said that no other Israeli prime minister in the past 46 years has been asked to stop building in Jerusalem, which would be unacceptable to his right-wing coalition partners.
He says he is willing to talk without preconditions, but has laid out a tougher stance on final status issues such as borders and Jerusalem than his predecessor, Ehud Olmert.
Israel has occupied East Jerusalem since 1967. It annexed the area in 1981 and sees it as its exclusive domain.
Under international law the area is occupied territory and the international community does not recognise Israel's annexation of East Jerusalem.