Prime Minister Benjamin Netanyahu addressed the peace process at the beginning of Sunday's cabinet meeting and said that "there is still much to be done."
"I hope we can bridge the gaps and reignite the peace process. We are not the ones mounting difficulties," he said.
Netanyahu is expected to travel to Egypt to meet with President Hosni Mubarak later in the day. He is also scheduled to meet with special US envoy to the Middle East George Mitchell on Monday.
Mitchell, who arrived in Israel late on Saturday, planned to meet Foreign Minister Avigdor Lieberman and President Shimon Peres later on Sunday and see Palestinian President Mahmoud Abbas in the West Bank city of Ramallah on Tuesday.
"Progress has been made on some issues and there are certain things in which we have yet to make progress," Netanyahu told reporters.
"I hope we will be able to narrow the gaps (during the talks with Mitchell) and perhaps to bridge them so that we can move forward in the diplomatic process.
A deal on halting building in settlements in the West Bank could pave the way for a meeting involving Netanyahu, US President Barack Obama and Abbas on the sidelines of the UN General Assembly in New York around September 23.
Abbas has said he would not restart peace talks with Israel, suspended since December, unless it committed to a settlement freeze as stipulated by a 2003 "road map" that charts a course toward Palestinian statehood.
"(Abbas) will tell Mr. Mitchell what he told him last time he met him: There will be no compromise in relation to settlements. Israel must halt all settlement activities including natural growth," Palestinian chief negotiator Saeb Erekat said.
Citing a need to accommodate the "natural growth" of settler families, Netanyahu has said construction of some 2,500 homes for Israelis in the West Bank would continue, and that Jerusalem would not be included in any settlement deal.
Addressing Friday's rocket attack on the Western Galilee region, the PM said Israel holds Lebanon responsible.
"I have said before that we will not accept attacks on Israel or terror directed against its citizens," he said, "It is clear that the (rockets) were fired from an area located south of the Litani River in violation of UN Resolution 1701."
Resolution 1701 ended the war between Israel and Hezbollah on the summer of 2006.
"The Lebanese government is responsible for all these violations and the attacks emanating from its territory," Netanyahu added.
Turning his attention to President Peres, who was discharged from the hospital earlier Sunday after collapsing at a Yitzhak Rabin Center function Saturday night, Netanyahu said, "Shimon cannot be stopped. I told him to meet with (special US Mideast envoy George) Mitchell and then get some rest.
"On behalf of all the ministers, I wish him good health," said the PM.