George Mitchell was talking after three-way talks in Egypt between the US, Israeli PM Benjamin Netanyahu and Palestinian President Mahmoud Abbas.

He said all sides had reconfirmed their commitment to the negotiations.

The talks come amid concern over the imminent expiry of Israel's partial ban on West Bank settlement building.

The two leaders have been joined in Sharm-el-Sheikh by US Secretary of State Hillary Clinton, who had earlier said Israel should extend its freeze on West Bank construction.

Palestinians say they will walk out if building on occupied territory resumes.

Mr Mitchell told reporters that Mr Abbas and Mr Netanyahu had held "serious discussions on the core issues" during the nearly two-hour meeting.

He gave few details of the talks but said all parties had "reiterated their intention to approach these negotiations in good faith and with a seriousness of purpose".

Mr Mitchell said the common goal remained "two states for two peoples," and that work was now underway to achieve a framework for that agreement.

Mr Abbas, Mr Netanyahu and Mrs Clinton later held a second round of talks with senior aides present, officials said.

The series of two- and three-way meetings in Sharm-el-Sheikh comes ahead of another trilateral meeting scheduled to take place in Jerusalem on Wednesday.