The shake-up followed a wave of kidnappings in the Gaza Strip that signaled a breakdown of authority.
"There is a crisis. There is a state of chaos in the security situation," said Prime Minister Ahmed Qureia after telling his Cabinet that he had given his resignation to Arafat, president of the Palestinian Authority.
Qureia, who has been in the post for 10 months, has been unable to carry out deep reforms in the Palestinian Authority to root out corruption - as long as Arafat remained the dominant power in the Palestinian territories.
He also has been frustrated by the failure to renew any peace process with Israel, say officials close to him. No Israeli-Palestinian summit was held during Qureia's time as prime minister.
Qureia sent his resignation letter to Arafat through an aide before meeting his cabinet, but Arafat scrawled a giant "X" over the paper with a pen, said a Palestinian official. Arafat told the prime minister he refused to accept it.
Qureia told his cabinet afterward that he would not withdraw the resignation, Jamal Shobaki, the minister of local government, told reporters.
The cabinet will reconvene Monday to continue deliberations, the prime minister said, and it was unclear what would happen if the stalemate continues between him and Arafat.
Officials said the cabinet meeting grew stormy at times. The interior minister, who is in charge of police and apparently was not consulted about the changes in the security infrastructure, walked out midway.
Israel had no comment on the swiftly unfolding events in Gaza and the West Bank. But Israel Army Radio quoted officials as saying the instability demonstrated again that Israel had no viable negotiating partner and must move forward with Prime Minister Ariel Sharon's plan tonext year.
But the chaotic events also were likely to encourage opponents of Sharon's plan who claim Israel cannot leave a security vacuum in Gaza and must stay.
Although failing to agree on the prime minister's future, Arafat and Qureia approved a series of steps to bring more than a dozen disparate security services under a more unified command.
They consolidated the services into three branches, but all will remain under Arafat's control. The specifics of the restructuring were not announced.
A reorganization of the splintered and often feuding security agencies was a primary demand of the United States as part of its moribund peace plan, known as the "road map."
Militant organizations said they were disappointed with the reorganization. Al Aqsa Martyrs' Brigades said the changes would fail to stem corruption that riddles the security forces, and threatened to take the law into their own hands.
The political crisis was precipitated by the kidnapping of two top security officials and four French charity workers in the Gaza Strip on Friday.
All were released unharmed after a few hours, but the abductions by militant organizations reflected the anger on the streets at the perceived ineffectiveness of the Palestinian Authority.
While the United States and Israel have tried to sideline Arafat, whom they see as the spoiler of Mideast peace efforts, Qureia's government has been paralyzed without Arafat's support for any of its decisions.
Qureia, also known as Abu Ala, was appointed in September 2003, when the first prime minister of the Palestinian government, Mahmoud Abbas, quit after just four months on the job. The two men were among the main negotiators of the 1993 Oslo peace agreement with Israel that created the Palestinian Authority.
Qureia's resignation was the third in two days. On Friday, two security chiefs also quit: the head of the Palestinian Intelligence Service, Maj. Gen. Amin al Hindi, and the head of Preventive Security in the Gaza Strip, Rashid Abu Shbak - both well known figures in the Palestinian hierarchy. Their resignations also were not immediately accepted.
In addition to changes in the structure of the security forces, Arafat issued a presidential decree replacing his national security chief and his national police chief.
Arafat appointed his first cousin, Mousa Arafat, as chief of public security. He replaced Abdel Razzak Al-Majaideh, who was given the title of security adviser.
Mousa Arafat was among the earliest members of the Fatah movement that launched the Palestinian national struggle in 1965.
The Palestinian leader also appointed Saeb al-Ajez as the new police chief for the West Bank and Gaza. He replaced Ghazi Jabali, one of the security officials who was kidnapped on Friday.