Violent clashes mark the anniversary of the intifada
The ceasefire was agreed during talks last week between Mr Arafat and the Israeli foreign minister, Shimon Peres.
But at least 12 Palestinians have been killed since Friday by Israeli troops, most in clashes marking the first anniversary of their uprising, or intifada.
The United States sees the ceasefire as a key element in securing Arab and Muslim support for the global coalition against terrorism.
Arrests demanded
The Israeli army will be free to "renew its strategy of attacks" in two days time if violence on the Palestinian side does not end, Israel radio reported on Sunday.
The decision came after the Israeli security cabinet met into the early hours of Sunday.
It is also demanding that Mr Arafat arrests a number of Palestinian militants on a list given to him by Mr Peres.
But the Palestinians deny receiving any such list, Reuters news agency reports, and, in their turn, accuse the Israelis of not fulfilling the terms of the ceasefire.
"The Israeli Government should have started [on Friday] to implement what we had agreed upon with Mr Shimon Peres... to remove their forces from our land to their original positions and to ease the siege," said Nabil Abu Rdainah, an aide to Mr Arafat.
The security cabinet did say it would go ahead and reopen some roads in the Palestinian territories and lift the closure of Jericho in the West Bank.
Accounts disputed
The Israeli ultimatum to Mr Arafat to restore calm came as its troops shot dead two Palestinians and wounded several others in the West Bank on Sunday.
A Palestinian taxi driver told journalists he was in a convoy taking a group of workers to the town of Tulkarm when they were forced to stop by rocks blocking the road.
The driver said that when the workers started moving the rocks, Israeli soldiers hiding in a nearby olive grove opened fire, the Associated Press news agency reports.
Israeli army radio said the convoy had failed to stop at a roadblock.
Anniversary casualties
Three Palestinians were shot dead and more than 150 injured by Israeli forces in the Gaza Strip and West Bank on Saturday, as the sides traded blame for the escalation of the situation.
On Friday - the first anniversary of the outbreak of the uprising - six Palestinians were killed in violent clashes and a seventh has subsequently died of his wounds.
On Saturday, tens of thousands of Palestinians joined a second day of protests in most major Palestinian towns, the largest gatherings taking place in Nablus, with 20,000 people, and Gaza, where 10,000 people crowded the streets.
The uprising broke out on 28 September 2001 when Palestinians, frustrated with the direction of the peace process, rioted after the then Israeli opposition leader, now Prime Minister, Ariel Sharon visited the site revered by Jews as the Temple Mount and by Muslims as the Haram al-Sharif or Noble Sanctuary.
Al-Aqsa mosque is the third holiest site in Islam, while to the Jewish people, who call it the area the Temple Mount, it is the holiest. The remains of the first and second Jewish temples are believed to lie beneath the site.
More than 600 Palestinians and 160 Israelis have died in the subsequent 12 months of violence.