* Two sides fail to resolve settlements dispute
* U.S. envoy says negotiations on a constructive path
* Palestinian spokesman describes talks as "serious" (Adds quotes from U.S., Palestinian officials; Israel saying it killed a Palestinian militant after grenade attack)
By Arshad Mohammed and Crispian Balmer
SHARM EL-SHEIKH, Egypt, Sept 14 (Reuters) - Israeli and Palestinian leaders failed in talks on Tuesday to resolve a dispute over Jewish settlement building but remain convinced they can reach a peace deal in a year, according to U.S. envoy George Mitchell.
No news emerged of any compromise on settlements after negotiations between U.S. Secretary of State Hillary Clinton, Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas.
With a 10-month Israeli moratorium on housing starts in settlements in the occupied West Bank due to end on Sept. 30,
Mitchell seemed upbeat in the face of Palestinian threats to quit the new talks if building resumes.
"President Abbas and Prime Minister Netanyahu continue to agree that these negotiations, whose goal is to resolve all core issues, can be completed in one year," Mitchell told reporters in Egypt's Red Sea resort of Sharm el-Sheikh.
"Today the parties have begun a serious discussion on core issues."
Mitchell said three-way talks would continue on Wednesday in Jerusalem, followed by lower-level discussions between Israeli and Palestinian teams in the coming days.
Netanyahu may fly to Washington for more talks early next week, Israel's state-owned Channel One television reported.
Neither Netanyahu nor Abbas made any immediate public comments. The meeting was their first since direct talks were relaunched in Washington on Sept. 2 after a 20-month hiatus, with a declared goal of resolving the main issues in a year.
The six-decade-old dispute revolves around settlements, security, borders and the fate of Palestinian refugees.
NO EXTENSION
Netanyahu, whose coalition government is dominated by pro-settler parties, said on Sunday he would not extend the construction moratorium but could limit the scope of further building in some settlements.
Echoing U.S. President Barack Obama's view, Mitchell said: "We think it makes sense to extend the moratorium, especially given that the talks are moving in a constructive direction."
He would not say whether there had been progress on the moratorium issue, saying only that "we believe that we are moving in the right direction overall".
Mitchell said Washington was aware of the issue's political sensitivity in Israel and had called on Abbas to "take steps that help, encourage and facilitate this (peace) process".
Palestinians say the settlements, built on land they want for a state, would deny them a viable and contiguous country.
Nabil Abu-Rdainah, a spokesman for Palestinian President Mahmoud Abbas, described the U.S.-sponsored talks as "serious" adding that there were "still real obstacles".
A senior U.S. official told reporters in Sharm el-Sheikh that Abbas and Netanyahu were "serious in wanting to find a way to continue these discussions".
"My hope and expectation is that they will find a way to do that but I don't want to either overstate or understate the case," he added.
Abbas has threatened to walk out of the talks if Israel does not extend the partial, self-imposed moratorium.
Clinton travelled on to Jerusalem and was to hold further talks there, in Ramallah and in the Jordanian capital Amman over the next two days.
Mitchell will visit Syria on Thursday and Lebanon on Friday in an effort to promote a wider peace between Israel and the Arab world, said a U.S. official who asked not to be named.
In continued violence, Israel said its troops had killed a Palestinian militant when a tank opened fire after a rocket-propelled grenade was shot from the Gaza Strip at its troops. Palestinian medics said four people were wounded.
The Democratic Front for the Liberation of Palestine, a militant faction, claimed responsibility for the incident. (Writing by Jeffrey Heller, Arshad Mohammed and Allyn Fisher-Ilan; Additional reporting by Marwa Awad in Sharm el-Sheikh, Edmund Blair in Cairo and Mohammed Assadi in Ramallah; Editing by Kevin Liffey)
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