The moratorium ran out on Sunday but the Palestinians have delayed a decision on whether to quit the talks until early next week, when Palestinian president Mahmud Abbas will meet Arab foreign ministers in Cairo.
"There are lots of doubts and obstacles on the way to peace. Everyone understands this," Netanyahu said in the statement.
"I and my government are committed to reaching a peace agreement ... that will safeguard the security and the vital interests of the state of Israel.
"I hope that the good talks that started with President Abu Mazen (Abbas) will continue in order to try to reach this goal."
The two men met at Netanyahu's weekend home in the coastal city of Caesarea, north of Tel Aviv, officials said.
Netanyahu has refused to renew the partial freeze on construction while urging Abbas to stick with the talks, which were relaunched on September 2 after a 20-month hiatus.
Abbas has said he will not formally respond to the renewal of building until the Cairo talks on Monday, but has warned Israel against continued construction in the settlements.
Netanyahu's office quoted Mitchell as saying he had come to bring a message of reassurance about Washington's commitment to reaching a comprehensive peace in the region, despite the numerous "potholes" along the way.
Mitchell, who met Israeli Defence Minister Ehud Barak shortly after his arrival, will head to the West Bank city of Ramallah on Thursday to meet the leaders of the Western-backed Palestinian Authority.
He will also hold talks with Arab leaders in the region ahead of Abbas's Cairo meeting.
Abbas is to hold consultations with leaders of the Palestine Liberation Organisation (PLO) as well as with the central committee of his Fatah party before heading to the Egyptian capital.
On Wednesday, European Union chief diplomat Catherine Ashton announced that she too would travel to the Middle East to meet Israeli and Palestinian leaders this week.
Ashton will arrive on Thursday on a three-day visit to meet Netanyahu, Abbas and Mitchell, her office said.
Ashton said in a statement that she had decided to fly to the region at the end of an official visit to the United States in the light of Israel's refusal to extend the settlement freeze.
"I have decided to travel directly from the United States to the Middle East as a matter of priority to urge both Israelis and Palestinians to find a satisfactory way for negotiations to continue and gather momentum," she said.
"As I have said, the EU regrets the Israeli decision not to extend the moratorium on settlements."
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