Quraya received verbal backing from the European Union on Monday with foreign policy chief Javier Solana's spokeswoman saying Solana would do all he could to support him.
“I don't want to see assassinations and demolitions of houses. I want to see a real ceasefire. These are my conditions,” Quraya told reporters at a press conference.
Quraya was speaking as Israeli occupation forces shot dead a Palestinian man they claimed was dressed in Israeli military fatigues and taking aim at them near the main Erez crossing point from the Gaza strip into Israel.
Palestinian security sources said the man was a member of the Al-Aqsa Martyrs' Brigade.
In other occupation violence Israeli forces demolished the family home of a Hamas activist in the West Bank refugee camp of Tulkaram in a dawn raid.
Quraya, who is the current speaker in the Palestinian parliament, was asked by Palestinian leader Yasir Arafat on Sunday to succeed Prime Minister Mahmud Abbas, who resigned on Saturday saying he had no support.
"It was (Abbas') despair at his inability to get the road map respected by the Americans, who did not keep their promise to put pressure on Israel"
Palestinian Authority representative in France
Still, Israel warned after Abbas’ resignation that it would not agree to the appointment of any Arafat ally as premier.
“Nothing would change while Yasir Arafat pulled the strings,” Foreign Minister Silvan Shalom said on a military radio station.
“The nomination of Abu Ala (Quraya), will not allow the peace process to make the least bit of progress while Arafat continues to pull the strings,” Shalom reportedly told US Secretary of State Colin Powell in a phone conversation.
US to blame
Meanwhile, the Palestinian Authority representative in France blamed the US for Abbas quitting.
Laila Shahid said America had failed to keep its word that it would pressurise the Israelis to make concessions.
“It was (Abbas') despair at his inability to get the roadmap respected by the Americans, who did not keep their promise to put pressure on Israel,” Le Parisien newspaper reported her as saying.
The future of peace negotiations lie in the balance as the US-brokered "road map is now in tatters". Abbas, appointed under both Israeli and US pressure, was seen as a solid negotiating partner.