The defections are a blow to Sharon's government
The National Union-Yisrael Beiteinu bloc and its two Cabinet ministers resigned from the coalition government on Monday in protest against the withdrawal of Israeli troops from the West Bank city of Hebron and plans to lift sanctions against Palestinians.
Mr Sharon's reaction was to tell the defectors: "You have caused me great distress, but you have given Arafat great satisfaction. You made his day."
Israel has been under pressure from the United States to save a fragile ceasefire agreed on 26 September.
The resignation of the ultra-nationalists does not endanger Mr Sharon's government, which still has a majority in the Israeli parliament.
But the prime minister - also a hardliner - now becomes more dependent on the moderate Labour Party.
Chance for talks
Seeking to reassure his own hardline followers, Mr Sharon told parliament: "I am not subject to any pressure and I do not intend to make any compromise on issues that endanger Israel's security."
Analysts say Foreign Minister Shimon Peres, a Labour stalwart and veteran peace advocate, may now be in a stronger position from which to restart peace talks with Palestinians.
Israeli troops, backed by tanks, occupied two hills overlooking Hebron on 5 October after Palestinian gunmen fired from there at Jewish settler enclaves in the centre of town.
The BBC's James Reynolds in Jerusalem says that Palestinians agreed to prevent further shooting.
Palestinian security forces have now entered the two neighbourhoods, set up checkpoints and taken over positions used by the gunmen.
Some Jewish residents of Hebron were arrested overnight during clashes with the withdrawing Israeli forces.
About 400 Jewish settlers live under heavy guard in the city of 130,000 Palestinians.
The two government members to resign were Tourism Minister Rehavam Ze-evi and National Infrastructure Minister Avigdor Lieberman.
Their exit leaves Mr Sharon's Likud party at the extreme right of the political spectrum in his government of "national unity".
Border crossings to re-open
Palestinians have complained that Mr Sharon has not implemented truce agreements.
They included lifting roadblocks and travel restrictions in the West Bank and Gaza Strip imposed after the current intifada - or uprising - erupted a year ago.
Moves towards lifting these restrictions led to the government defections.
Israel has reportedly also agreed to re-open border crossings with Egypt and Jordan and to resume gasoline supplies to the Palestinian Authority.
Israel, for its part, complains that Mr Arafat has failed to halt militant Palestinian violence against Israelis.