(Adds Lebanese soldier death, paragraph 7)

By Tom Perry

BEIRUT, June 20 (Reuters) - Palestinian mediators on Wednesday presented the Lebanese army with a plan to end a month of fighting with al Qaeda-inspired militants at a Palestinian refugee camp in northern Lebanon.

The plan was drawn up after the mediators -- a group of Muslim clerics -- met Fatah al-Islam militants holed up at the Nahr al-Bared camp in a bid to quell Lebanon's worst internal violence since a 1975-1990 civil war.

"We hope that the response will be positive and swift," Sheikh Mohammed al-Haj, one of the mediators, told Reuters after meeting the head of military intelligence.

He declined to outline the proposals but a Palestinian political source said on Tuesday a plan to end the fighting included the disbandment of Fatah al-Islam and the deployment of a security force from the mainstream Palestinian factions.

The government has demanded the surrender of Fatah al-Islam, which it accuses of starting the conflict by launching unprovoked attacks on army positions on May 20. Fatah al-Islam has always said it has acted only in self-defence.

The rattle of automatic gunfire could be heard at the camp during intermittent clashes on Wednesday. The army fired on militant positions with artillery, witnesses said.

The army said one more Lebanese soldier had died on Tuesday to bring the total death toll since fighting erupted on May 20 to at least 164 -- 75 soldiers, at least 57 militants and 32 civilians.

The army has slowly seized an area previously controlled by the militants, without entering the camp's official boundaries. Security forces are barred from going into Lebanon's 12 Palestinian refugee camps by a 1969 Arab agreement.

Most of the camp's 40,000 residents fled in the early stages of the fighting. Most went to the nearby Beddawi refugee camp.

UNRWA, the U.N. agency which cares for Palestinian refugees, said mines and booby traps inside the camp must be dealt with before the displaced people can go home once the fighting stops.

"We don't want people rushing back because we are afraid they may be endangered. We have to check on the buildings to see if they are structurally safe," UNRWA spokeswoman Hoda Samra said. (Additional reporting by Nazih Siddiq at Nahr al-Bared)

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