Al Jazeera's Mike Hanna, reporting from Jerusalem, said: "We've heard George Mitchell saying there has been progress, but this does not disguise the fact that there remains substantial differences between the approach of the Obama administration and that of Israel.
"Very clearly there are deep disagreements over several issues, notably the question of ongoing Israeli settlement activity in the West Bank.
"The whole issue here at the moment is that this is a new US administration.
"No party wants to be seen as being a spoiler in any of this, so each of the parties is going out of their way to show how flexible they can be.
"... this is very much part of a window of opportunity perhaps that George Mitchell has seen, to use the newness of his administration to persuade all the parties involved not to be seen as spoilers in what is a completely new process."
Israeli media reports over the past several days have said that the sides are close to reaching a compromise that would see Israel agree to a temporary settlement freeze, but continue construction projects already under way.
Tuesday's meeting was part of Mitchell's regional tour in which he has held talks with leaders of Syria, Egypt and the Palestinians in four days.
"President [Barack] Obama's vision is of a comprehensive peace in the Middle East which includes peace between Israel and the Palestinians, between Syria and Israel, and between Israel and Lebanon," Mitchell said after talks with the Israeli premier.
"Obama's vision is of a comprehensive peace in the Middle East [which includes] peace between Israel and the Palestinians, between Syria and Israel, and between Israel and Lebanon"
US envoy to Middle East
Such a deal would also see "a full normalisation of relations between Israel and all its neighbours in the region," Mitchell said, who played a key role in brokering the 1998 peace accord in Northern Ireland.
To move toward such a deal - which would put an end to the decades-old Arab-Israeli conflict - all sides "must take steps, some of them difficult some of them controversial," the US envoy said on Monday after talks with Mahmoud Abbas, the Palestinian president.
"For the Arab states, that means meaningful steps toward normalisation of relations with Israel," he said.
"For the Palestinians, it means expanding and improving their security forces, to take action against incitement and to refrain from any words or deeds that may make it more difficult to move quickly toward successful negotiations.
"For Israel, that means making possible improved access and movement and economic growth for Palestinians ... and dealing with difficult issues like settlement and outposts."
Letters for peace
Backing up the envoy's call, the White House confirmed Barack Obama, the US president, had recently sent letters to Arab governments urging confidence-building measures to create a climate for peace negotiations.
The written appeals for conciliatory moves, reportedly made to at least seven states in the region, coincided with US officials lobbying Israel to freeze settlement activity on occupied territory.
Mitchell is one of three senior US officials who are visiting Israel and the region this week as part of Washington's drive to jumpstart the moribund Middle East peace process.
Israel and the Palestinians relaunched negotiations after a break of more than six years at an international conference in the United States in November 2007, but the talks made little progress before being suspended amid Israel's assault on Gaza earlier this year.