It was a further sign of possible tension brewing between Abbas and Qorie. Abbas has also rejected a planned London conference on Palestinian reform endorsed by Abbas, saying what was really needed now was a peace conference.
Qorie said efforts to achieve a cease-fire and advance peacemaking largely depended on Israel, which by contrast has put the onus on Palestinians to lay down arms as a condition for internationally-sponsored negotiations to begin.
"If there was a credible, serious peace process and a real chance to reach a just and comprehensive settlement, the Palestinians should immediately start negotiations and stop violence," Qorie told Reuters in an interview.
For Palestinians, a just outcome is a state in all of the Israeli-occupied West Bank and Gaza with East Jerusalem as its capital. Israel aims to quit tiny Gaza but hold on to large West Bank settlements for good and rules out dividing Jerusalem.
"If there is a serious international effort to enable the Palestinians to achieve statehood, non-violence is an option that has to be tried. If there is a real chance for peace, we will not waste it," said Qorie, like Abbas seen as a moderate.
Abbas, the heavy favourite to succeed the late Yasser Arafat in a January 9 presidential election, has campaigned on a platform of non-violence while courting militants by vowing to compromise on the conditions he set for peace.
CREDIBILITY GAP: Abbas and Qorie both lack Arafat's legendary stature and charisma, leaving both dependent on Israeli gestures to acquire the street credibility needed to bring militants to heel.
Israeli officials privately do not expect Abbas or Qorie to be able to put a total stop to violence in the near term, raising doubt about chances for fresh peace negotiations soon after Abbas's anticipated election.
Bloodshed has ebbed throughout the West Bank since Arafat's November death but not in Gaza, where militants have cranked up rocket and mortar fire at settlements in hope of claiming "victory" once Israel carries out its planned withdrawal.
That fighting has tempered new international hopes of a Middle East peace breakthrough after the death of Arafat, who was boycotted by Israel and the United States as an alleged mastermind of violence. Qorie accused Israel, with its continued military incursions against Gaza militants, of undermining Palestinian Authority efforts to rein in the gunmen.
"We are holding talks with Hamas and others to achieve quiet, but Israel aborts every effort to control the situation by continuing the raids and assassinations (of militant leaders) in Palestinian areas," he said.
Qorie said the Authority would also soon implement a law to combine 12 security services, which have been linked with militant and internal gang violence, into three.
"Ending internal chaos is our first priority because it harms our national cause," he said.