Netanyahu and Abbas meet in Sharm el-Sheik

The leaders of Israel and the Palestinian Authority held nearly two hours of face-to-face talks in this Red Sea resort on Tuesday in a second round of negotiations that delved into the core issues dividing them but did not yet break an impasse over Jewish settlements.

Prime Minister Benjamin Netanyahu has ruled out extending the moratorium, while the president of the Palestinian Authority, Mahmoud Abbas, has threatened to walk out of the talks if Israel allows it to expire, New York Times reports.

"Today the parties have begun a serious discussion on core issues," U.S. Middle East envoy George Mitchell said after the meeting in the Egyptian resort of Sharm el-Sheikh, which lasted almost two hours. He declined to give details of what was discussed.

Clouding the talks is the Sept. 26 expiration of a temporary halt Netanyahu declared on West Bank settlement building, which President Barack Obama asked him last week to extend. Abbas has said he will abandon talks if construction resumes. Netanyahu has said there has been no change in plans to let the freeze expire, according to Bloomberg.