U.S. Middle East envoy George Mitchell on Tuesday provided a cautious note of optimism as Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas wrapped up the second round of direct peace talks in the Egyptian resort of Sharm el-Sheikh.

Israeli Prime Minister Benjamin Netanyahu, U. S. Secretary of State Hillary Clinton, Palestinian President Mahmoud Abbas and U.S. peace envoy to the Middle East George Mitchell hold talks in Egypt's Red Sea resort of Sharm El-Sheikh, Sept. 14, 2010. Egypt is hosting the second round of the Palestinian-Israeli peace talks. [Xinhua]

Both leaders "negotiated in good faith and confirmed their vision of a two states for two peoples solution," Mitchell said at a post-summit press conference.

Netanyahu and Abbas had also discussed some "core issues," the borders of a future Palestinian state, Palestinian refugees and the status of Jerusalem, which will dominate the year-long negotiations for a final peace deal, said Mitchell.

Mitchell, however, offered no comforting news of progress on the complex issue of the West Bank settlement construction moratorium, but did repeat U.S. President Barack Obama's recent call on Netanyahu to extend it after its official expiration on Sept. 26.

"We think it makes sense to extend the moratorium," Mitchell said.

While Mitchell did not touch upon the specifics of a possible solution to the debate, which many believe can bring about a premature end to the recently-launched peace talks, he said he and U.S. Secretary of State Hillary Clinton believed the talks are " generally moving in the right direction."