Qureia has to complete the job by midnight Tuesday. Failure could trigger a new political crisis, deepen the deadlock over U.S.-backed "road map" peace plan and hold up Qureia's planned meetings with Ariel Sharon and leaders of Hamas.
In the West Bank, a 16-year-old Palestinian blew himself up near Israeli soldiers searching for him in the village of Azzoun, near Israel. The suicide bomber, Sabih Abu Saud from the city of Nablus, killed only himself and slightly injured a soldier.
About two hours earlier, Israeli security forces had gone on high alert after receiving information that a suicide bomber planned to infiltrate Israel, reports CBS News Correspondent Robert Berger. The army believes the terrorist decided to target soldiers because security was too tight to sneak into Israel.
He was sent by the Al Aqsa Martyrs' Brigade, an armed group with ties to Yasser Arafat's ruling Fatah movement. The youngster's father, Kamal, said that "he was just a little boy and those who sent him should have left him alone."
In the West Bank town of Ramallah, Qureia met with Arafat and other members of the National Security Council as part of consultations on a new Cabinet.
Qureia and Arafat remain at odds over the choice of interior minister, who will play a key role in any possible action against armed groups. At the core of the dispute is Arafat's refusal to relinquish control over some of the security forces.
For the past month, Qureia has presided over a small emergency Cabinet that operated without parliamentary backing and was virtually paralyzed. Over the weekend, Arafat asked Qureia to stay on the job and form a regular government.
Once he has a government, Qureia plans to hold separate talks with Israeli Prime Minister Ariel Sharon and leaders of the Islamic militant Hamas, to try to break the months-locked deadlock over implementation of the road map. Israeli media reported that a Qureia-Sharon summit could take place by the weekend.
In recent days, there has been a slight easing of the tensions between Israeli and Palestinian leaders, following a month of particularly stringent Israeli travel bans on Palestinians.
Israeli Defense Minister Shaul Mofaz confirmed that he met Sunday with Palestinian Finance Minister Salam Fayad. Mofaz said more high-level meetings would be held once Qureia has formed a government.
Qureia has said his top priority is to negotiate a truce with Israel. Sharon has rejected the idea, saying the Palestinian Authority must first dismantle militant groups, as required by the "road map" peace plan.
However, Sharon has come under increasing criticism at home, including from his army chief, for pursuing a policy of military strikes, without pushing hard to resume peace talks. Last week, Sharon said he was open to holding talks without conditions, a turnaround from his earlier demands that violence must stop first.
Hamas, in turn, said it was only willing to agree to a partial truce. Abdel Aziz Rantisi, a Hamas leader, said the group would be willing to halt attacks on Israeli civilians, but not on soldiers and settlers in the West Bank and Gaza Strip.
"The only thing which can be offered is to continue resistance, but to avoid (spare) civilians from both sides," Rantisi said. "If the enemy does not accept it, the resistance will continue in a comprehensive level."
Israel has made it clear that a partial truce would not be acceptable, and Qureia has said he hopes to reach a comprehensive cease-fire.
Qureia's task of forming a Cabinet did not appear any easier Monday than a month ago when, at the last minute, he backed away from presenting his proposed team to parliament for approval because of intense political wrangling.
Despite the difficulties, Saeb Erekat, the chief Palestinian negotiator, said Monday he is believes a new government can be formed within two days.
"It's very realistic," Erekat said, but acknowledged that "there are still some problems concerning the interior minister."
If Qureia does not form a Cabinet by midnight Tuesday, the Palestinians would effectively be without a government.
In other developments Monday, parliament approved hard-liner Rafik Natche, a former agriculture minister, as parliament speaker. The post is important because the speaker would become acting leader of the Palestinian Authority if Arafat steps aside or dies. Qureia left the speaker's post when he was made prime minister.