JERUSALEM (Reuters) – Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas hold a second day of talks on Wednesday to try to overcome a row over Jewish settlement building that could sink their push for peace.

Netanyahu will first meet separately with U.S. Secretary of State Hillary Clinton and Abbas will join them in the afternoon for three-way talks that will also be attended by Washington’s Middle East envoy George Mitchell.

The two leaders failed in talks on Tuesday in Egypt to find a compromise over the settlements, but Mitchell said the pair discussed several core issues that split the two sides and said that they were convinced they could reach a deal within a year.

A 10-month Israeli moratorium on new housing construction in West Bank settlements expires on September 30 and Palestinians have said they would quit the U.S.-brokered talks if building resumes.

Mitchell said after meetings in the Egyptian Red Sea resort of Sharm el-Sheikh that he believed they were “moving in the right direction overall.”

The status of Jerusalem, the fate of Palestinian refugees, the borders of a future Palestinian state and security arrangements are the main issues that the two leaders would have to resolve to secure a permanent peace deal.

This latest round of direct talks were relaunched at the start of September after a 20-month hiatus.

Israeli media reported that Netanyahu may fly to Washington early next week, with speculation that U.S. President Barack Obama may get involved to try to resolve the settlement impasse.

Netanyahu, whose coalition government is dominated by pro-settler parties, has said he would not extend the freeze but could limit the scope of building in some settlements.

Palestinians say the settlements, built on land they want for a state, would deny them a viable and contiguous country. The settlements are on territory Israel captured in the 1967 Middle East war and are deemed by the World Court to be illegal under international law.

The talks could also be derailed by continued violence. Palestinian militants in the Gaza Strip fired a rocket and two mortar bombs into Israel on Wednesday, the Israeli army said.

The Islamist group Hamas, which seized control of Gaza in 2007 from forces loyal to Abbas, is opposed to Israeli talks.

After Clinton completes talks in Jerusalem, Ramallah and Amman over the next two days, Mitchell plans to travel to Syria and to Lebanon to work towards a wider peace, an official said.