The explosions have left the Palestinian leader trapped, under intense pressure to act but faced with an array of equally unpalatable choices.
In an emergency meeting after the bombing, which left 15 dead and more than 170 injured, Israeli Prime Minister Benjamin Netanyahu and his security Cabinet produced a list of demands for Mr Arafat, "first and foremost to fight the terror groups and their infrastructure". Israel blames the militant Palestinian organisation Hamas for the bombing, and Mr Arafat and his police for letting Hamas get away with it.
Mr Arafat must extradite Palestinians wanted by Israel, must take "immediate steps" against high-ranking officials in his police force who are accused of planning attacks on Israelis, and must resume full co-operation with Israeli security services - and until he does, Mr Netanyahu said, there will be no more peace talks.
The Israeli Prime Minister called his demands reasonable, indeed, basic, in the context of the peace process; he was echoed by US Secretary of State Madeleine Albright and most of the international community. But Israel could hardly have given Mr Arafat a more impossible list of demands.
"There is simply no way he can do this," said Dr Khalil Shiqaqi, head of the Centre for Palestine Research and Studies, a Nablus think-tank. "Israel has weakened him so far, he is fighting for his own survival, and Hamas is as much a threat to him as it is to Israelis. If he does what Israel demands, he will be discredited past any recovery."
A year and a half ago, after a series of bus bombings that left 66 Israelis dead and gutted the peace process, Mr Arafat was able to take forceful action against Hamas and Islamic Jihad; and indeed, he seriously damaged the infrastructure of both organisations. But back then, the PLO leader had just won election as president with 88 per cent of the vote; he had public support, because the Israeli army had recently left the West Bank cities; the economic situation was good and the peace process was going well.
"Today, none of those things is true," said Dr Shiqaqi. "Plus, he is facing wide allegations of corruption and human rights abuses."
Palestinian police have made some arrests in the West Bank towns they control, but Mr Arafat is in no position to start another crackdown on Islamists. While the suicide bombings are not condoned by the majority of Palestinians, Hamas as a political party does have a solid support base. Nor will it serve Mr Arafat now to be seen as caving in to Israeli demands. "He is not going to put himself on the line when Israel is doing everything it can to discredit him," Dr Shiqaqi said.
So what will he do? Palestinian commentators believe Mr Arafat will take some localised action against Hamas and Jihad, when he finds out who was responsible for this bombing. Then, he will have to wait out the Israeli anger, hoping his own population does not erupt first.
Palestinian political analyst Ghassan Khatib argues that Israel is being unrealistic in asking Mr Arafat to take measures now. "They don't understand that the violence is a result of Israeli policies, not a cause of the stagnation of the peace process," he said, citing settlement building and the closure of the Palestinian territories in particular. "Israelis need to ask themselves why 20-year-olds are so eager to commit suicide."
Yesterday morning, Israeli security forces arrested the families of two young men from the West Bank village of Dharriyeh and took them for genetic testing, attempting to identify the corpses of the suicide bombers. The two young men, Saled Al-Teil and Majid Qaissiyeh, disappeared from Dharriyeh 15 months ago and were the subject of a joint PA-Israeli search, because it was feared they might be planning such an attack. They were not known to be members of Hamas, although their families said they were "quite religious", and neither was married, in keeping with the profile of the typical suicide bomber.