"His first step must be to make the strategic decision to dismantle the infrastructure of terrorism," said Israeli Foreign Minister Silvan Shalom on Tuesday.
"We will judge any Palestinian prime minister by his actions. He will have to decide whether he stands with Arafat or whether he stands against terrorism," Shalom said.
In Washington, the US State Department on Tuesday reiterated the administration's refusal to deal with Arafat, or any of his allies who could not deal strongly with security issues.
The comments maintain pressure on Quraya, who must walk a tightrope between satisfying US demands and retaining domestic political and popular support - a feat his predecessor did not manage.
Avoiding power struggle
To avoid any conflict between Quraya and Arafat, new arrangements for control of the myriad Palestinian security apparatus are being drawn.
The plan aims to prevent Quraya becoming sucked into the kind of power struggle Arafat experienced with outgoing premier Mahmud Abbas.
Former Prime Minister Mahmud
Abbas enjoyed limited authority
"We are moving towards the creation of a supreme national security council which would decide on the security policies of the (Palestinian) authority, which would then be implemented by the interior ministry," said one Palestinian official, speaking on condition of anonymity.
Arafat and Quraya have also agreed that the future interior minister, the head of security services, Amin al-Hindi, the director of national security in Gaza, Abd al-Razzak al-Majaidah, plus his West Bank counterpart, Ismail Jabr, would all sit on the council.
"I think that President Arafat will give the prime minister and his interior minister the freedom to put into place the policies of the council in a manner that they judge appropriate," another official said on condition of anonymity.
The name most frequently touted to become the next interior minister is Nasir Yusuf, a general who is close to Arafat and a member of the Fatah central committee.
Abbas was given control of three of the many Palestinian security branches: the civil police, civil defence and preventive security force.
But the 35,000-40,000 strong national security force and other branches such as intelligence, the navy and border police, remained under Arafat's command.
The US-backed road map for peace calls for the security services to be unified under a single command. Abbas had demanded more control over the security services so he could rein in resistance groups. His failure to win this control contributed to his fall.