Arafat and Prime Minister Mahmoud Abbas have disagreed in the past week on key appointments and control of Palestinian security forces, which under the U.S.-backed "road map" peace plan are required to dismantle militant groups.
"I think we must put an end to this internal crisis. We have to find a formula to organize relations between the presidency and (Abbas') council. We face a serious challenge from the Israelis," Palestinian Information Minister Nabil Amr said at a news conference in the West Bank town of Ramallah.
A senior Israeli official, speaking on condition of anonymity, said Israel told U.S. officials it will not deal with Arafat "or any marionette that he puts in place" of Abbas.
Arafat reluctantly appointed Abbas, his PLO deputy, as the Palestinians' first prime minister in April under pressure from Israel and the United States, which have tried to sideline Arafat and want an alternative leader.
Palestinian mediators were shuttling between Arafat and Abbas seeking to try to bridge their differences, officials said.
"The situation had reached a stage where it was not acceptable to anybody," said Ahmed Qureia, speaker of the Palestinian parliament. "It has its effects on the entire process, and that's why it is very dangerous."
A Palestinian parliament meeting scheduled for Monday was pushed back to Thursday. Abbas was trying to garner support after the latest violence and was to address legislators on his achievements during his first 100 days in office.
The disputes persisted a day after Israel killed a leading Hamas militant and his assistant in a helicopter missile strike in the Gaza Strip on Saturday. Israel has killed 10 Hamas members in five missile strikes in Gaza since a Hamas suicide bomber killed 21 people in Jerusalem on Aug. 19.
In the latest attack, Israeli helicopters fired four missiles at a pickup truck carrying the two militants, witnesses said. Two bystanders were wounded.
Israeli troops on Saturday also killed an 8-year-old girl and wounded seven other Palestinians with submachine gun fire in the Gaza Strip's Khan Younis refugee camp, witnesses and hospital officials said. The girl, Aya Fayad, was shot in the chest while riding her bicycle, witnesses said.
Soldiers fired at an area where Palestinian militants were detonating roadside bombs on a patrol route, the army said. Militants in the same area later fired three mortar shells at a Jewish settlement, damaging a house but injuring no one, the army said.
Hamas claimed responsibility for a sniper attack Sunday that wounded an Israeli man in his car near a Jewish settlement in the Gaza Strip. The man was in critical condition.
Palestinians have been firing mortars and homemade rockets in recent days at Israeli settlements in Gaza and towns in Israel.
After Saturday's missile strike, some 5,000 Palestinians marched in a funeral procession in Gaza urging revenge.
An armed Hamas member told mourners that Israeli Prime Minister Ariel Sharon "will soon receive a very painful message from the Hamas military wing in retaliation for his crimes against the Palestinian people."
Israel will continue to target militants so long as the Palestinian Authority does not act to rein them in, Foreign Ministry official Gideon Meir said.
"We cannot expose our children to the continuous massacre which we witnessed in Jerusalem," Meir said, accusing Abbas of failing to fulfill commitments under the U.S.-backed "road map" peace plan.
The Aug. 19 suicide bombing combined with Israel's missile strikes has left the plan in tatters and destroyed a cease-fire militant groups declared on June 29.
Abbas has said Israel's strikes make it virtually impossible for him to crack down on militant groups.
On Saturday, dozens of armed men loyal to Arafat turned out in the Gaza Strip to try to block the replacement of one of Arafat's supporters at the head of a civil service department.
Abbas' Cabinet picked Sakher Basseso, governor of northern Gaza, to take over the post. But ousted Arafat loyalist Mohammed Abu Sharia has refused to go.
For nearly two years, Israeli troops and threats have kept Arafat stranded at his sandbagged West Bank headquarters, which has been heavily damaged by tank shells and bulldozers.
U.S. officials have urged the 74-year-old Arafat to give Abbas full control of security forces to facilitate a crackdown on militants, but Arafat has resisted.