Quraya's chief of staff said he had won effective control over police and internal security agencies.
Arafat's move, initially disclosed by a pro-reform committee of legislators after a meeting with him, followed an unprecedented explosion of unrest over high-level inaction on demands for anti-corruption reforms.
Tuesday's deal leaves Arafat in charge of national security and intelligence which encompass the bulk of Palestinian security personnel.
"The president rejected my resignation and I will comply," Quraya said after 10 days of turmoil that raised fears of a descent into anarchy in the West Bank and Gaza.
"I hope I will be up to this confidence and cooperate with [Arafat] in carrying out this very difficult responsibility," Quraya said after a cabinet session from which he and the president emerged smiling, each kissing the other on the cheek.
Arafat would address the Palestinian people soon to provide details of the deal, Quraya added.
"The cabinet has been given powers to exercise its duties... This is a good step"
Hasan Abu Libda,
Quraya's chief of staff
"The cabinet has been given powers to exercise its duties. We are speaking now of decrees and decisions that will be announced very soon," said Hasan Abu Libda, Quraya's chief of staff.
"This is a good step. In the next few days and weeks we will see action permitting the government to play its role."
Quraya had wanted to bow out over his inability to pursue reforms, especially to security organs under Arafat's control.
Palestinians killedMeanwhile, two Palestinians were killed in a clash with Israeli troops in a neighbourhood on the edge of Gaza City.
The victim was killed in clashes
with Israeli forces
The Israeli forces took rooftop positions on the house of Muhammad Jundiya and opened fire around it, killing two Palestinians and injuring four others, including a 10-year-old child, Aljazeera's correspondent reported.
After the assault, the Israeli occupation forces withdrew.
Israeli troops also fired along the border in Rafah, injuring two Palestinians, one seriously, said the correspondent.