The US has launched a new effort to finalise terms for fresh negotiations between Israel and the Palestinians.
Mr Mitchell has been discussing the expansion of Jewish settlements in the West Bank - a key stumbling block.
He said: "It is our intention to conclude this phase of our discussions in the very near future."
"This will enable us to move on to the next and really the more important phase," he added.
Meanwhile, Israeli Prime Minister Benjamin Netanyahu has met Egyptian President Hosni Mubarak in Cairo.
Mr Netanyahu said on Sunday work still needs to be done to narrow differences before peace talks can resume.
Mr Mitchell, who arrived in Israel on Saturday, has been trying to secure a deal involving a halt to settlement building and Arab nations taking steps towards recognising Israel.
"While we have not yet reached agreement on many outstanding issues, we are working hard to do so," Mr Mitchell said after talks in Jerusalem with President Shimon Peres on Sunday.
The US hopes that the renewed impetus will lead to a meeting between Israeli and Palestinian leaders on the sidelines of the UN General Assembly meeting in New York later this month.
Mr Peres said there was "an urgency to resume negotiations".
Israeli-Palestinian peace talks have been suspended since December.
After the talks between Mr Mubarak and Mr Netanyahu in Cairo, the Egyptian president called on Israel "to stop all settlement activity, including 'natural growth' settlements," his spokesman said.
A statement from Mr Netanyahu's office said the men had "discussed the challenges facing the region and the need for all sides - Israel, the Palestinians, Arab states and the international community - to contribute their part to advancing the peace process".
Mr Mitchell met Israel's foreign minister and defence minister on Sunday.
'Obstacles'
Before flying to Cairo, Mr Netanyahu said of the peace push: "There are things where there has been progress and things where there still has not been.
"I hope we will be able to narrow the gaps and perhaps bridge them so we will be able to get peacemaking moving."
He added it was not Israel that was "setting up obstacles" to talks.
Palestinian leader Mahmoud Abbas insists he will not meet his Israeli counterparts until there is a freeze on new settlements in the West Bank.
The settlement of occupied territory is illegal under international law but Israel last week said it had given permission for 455 new homes to be built.
The move prompted Mr Abbas to say that there was no point attending a summit with Mr Netanyahu.
The White House also criticised the settlement decision. President Barack Obama has previously said he wants all settlement activity to stop.
Israel has indicated that it will be willing to consider a temporary halt to granting permission for further construction.
President Peres met Mr Mitchell hours after being discharged from hospital a day after fainting on stage.
Mr Peres, 86, collapsed briefly while standing at a lectern answering questions in Tel Aviv.
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