The Palestinian Authority has been plunged into a political crisis by a spate of kidnappings in Gaza.
Arafat has been under pressure to reform security
Prime Minister Ahmed Qurei spoke of an "unprecedented chaos" and tendered his resignation and that of his government.
But Palestinian leader Yasser Arafat rejected the move and announced an overhaul of his security forces.
The Palestinian government is going into a rolling emergency session for the next 48 hours to try to resolve the situation.
A period of political instability that could lead to a worsening of security in Gaza appears inevitable, says the BBC's David Chazan in Jerusalem.
A state of emergency has been declared in Gaza.
Lawlessness has been increasing as militant groups appear to be trying to strengthen their positions before a planned Israeli withdrawal from Gaza, our correspondent says.
That, combined with a lack of clear directives from Mr Arafat, has led to the prime minister's strong language, he says.
Mr Qurei described the security situation in Gaza as "a real disaster, a real catastrophe, and an unprecedented lawlessness".
After offering to resign, he chaired an emergency meeting of his cabinet to discuss the government's response.
No one is quite sure what will happen after the 48 hours of talks on the crisis, one Palestinian minister told the BBC.
Mr Qurei wants Mr Arafat to grant him more powers to deal with the worsening security situation.
If the prime minister says he is being hampered in carrying out his duties - including maintaining law and order - "he should either claim his powers" or resign, Palestinian lawmaker Hanan Ashrawi told the BBC World Service's Newshour programme.
Mr Arafat said he was overhauling the eight existing Palestinian security services - a long-standing international demand.
His aide, Nabil Abu Rudeina, said Mr Arafat had decided "with immediate effect" to cut the security services to three - police, general security and the intelligence service, AFP reported.
Mr Arafat has appointed his nephew Musa as overall security chief. Maj Gen Saeb al-Ajez replaces Ghazi Jabali - the Gaza police chief who was the first to be kidnapped on Friday.
His abductors, Jenin Martyrs' Brigades, had demanded that he be investigated in connection with corruption allegations.
Amin Hindi, the head of Palestinian general intelligence, and his colleague Rashid Abu Shabak, the preventive security chief in Gaza, had offered to resign "because of the state of chaos and the lack of action by the Palestinian Authority to make reforms".
The gunmen who took the hostages complained of corruption
But Mr Arafat did not accept the resignations and is said to have reappointed Mr Hindi.
Among those kidnapped on Friday were four French aid workers and another Palestinian official, Colonel Khaled Abu al-Ula. They have all been released.
Security has been reinforced around key buildings, but otherwise Gaza City appears normal.