(Reuters) - Lebanon and Israel need to make progress demarcating their border to avoid a repeat of a cross border clash in which four people were killed this month, the U.N. special coordinator for Lebanon said on Monday.

Michael Williams, speaking before the Security Council was expected to approve extending the mandate for U.N. peacekeepers in south Lebanon, said an Israeli withdrawal from the border village of Ghajar would also help reduce tension.

Williams told Reuters the Aug. 3 clash had alarmed countries which contribute forces to the 12,000-strong UNIFIL peacekeeping mission, and there was a need to build up trust between Lebanon and Israel "which has obviously taken quite a knock".

A senior Israeli officer, two Lebanese soldiers and a Lebanese journalist were killed in the shooting, the bloodiest border confrontation since Israel's 2006 war against Hezbollah.

After the incident the two sides disputed whether Israeli troops had crossed the border into Lebanon, but UNIFIL said they were operating on the Israeli side of the "blue line", or U.N.-mapped border, when the shooting erupted.

Williams called for progress "on questions like the marking of the blue line. At the moment there's only about a fifth, about 30 km (20 miles), which has been marked."

An Israeli withdrawal from the northern part of the divided border village of Ghajar "would do a lot to help restore trust as well," he added in a telephone interview.

'DISQUIET' OVER CLASH

Williams said countries which contribute forces to UNIFIL were strongly committed to the peacekeeping operation in Lebanon, but added that the border clash "will have caused a lot of disquiet in capitals".

Governments also had to balance competing demands to support other military operations, including in Afghanistan, and faced domestic pressures to cut back spending during an economic recession, he said.

"But my own reading of the member states, particularly the Europeans -- France, Italy and Spain, (is that the commitment) is still strong," he said, referring to three of the main troop contributors to UNIFIL.

UNIFIL was set up in 1978 and expanded in 2006 to monitor the end of hostilities between Israel and Hezbollah.

Israel has criticised the U.N. peacekeeping operation for not stopping weapons it says are still flowing to Hezbollah guerrillas. The United Nations say that is the responsibility of Lebanese authorities.

Williams said he would travel to France, Spain and Britain later this week and would discuss regional diplomatic efforts which could reduce the danger of renewed conflict between Israel and Lebanon.

"Lebanon is not an island and the regional picture is important," he said. "I hope the talks that begin in Washington between the Israelis and Palestinians on Thursday will have a positive impact."

He said any move towards a resumption of Israeli-Syrian peace talks, however remote a prospect that might appear, would also help reduce tension. (Editing by Jon Hemming)