The march comes in the wake of a spate of kidnappings which targeted Palestinian security officials and French aid workers late on Friday, triggering a series of resignations and fears of a breakdown of authority.
The majority of demonstrators are thought to be activists from offshoots of Arafat's Fatah movement.
"Even it means we will behead people, we are not afraid," shouted demonstrators, referring to the tactics employed by various Iraqi factions trying to have their demands met for a pullout of occupation forces.
On Friday, members of the Janin Martyrs' Brigade briefly kidnapped the police chief in the occupied Gaza Strip and West Bank, Ghazi al-Jabali.
He was released only after securing assurances he would be replaced.
Resignations, cabinet reshuffled
Amid the political instability, Palestinian Prime Minister Ahmad Quraya submitted his resignation on Saturday, but it was rejected by Arafat.
"There is a crisis. There is a state of chaos in the security situation," said a frustrated Quraya. The Palestinian premier, who has been in office for ten months, told his cabinet he would not withdraw his resignation.
Cabinet deliberations are expected to continue on Monday.
Quraya was the third Palestinian leader to submit his resignation within 24 hours.
Palestinian groups reject the
appointment of Arafat's cousin
The head of the Palestinian Intelligence Service, Major General Amin al-Hindi, and the head of Preventive Security in the Gaza Strip, Rashid Abu Shabak - both well-known figures in the Palestinian hierarchy - quit on Friday.
Their resignations were also not immediately accepted.
Arafat reshuffled the security apparatus in response to the demands outlined by al-Jabali's kidnappers and appointed the relatively unknown Saib al-Ajaz as the new police chief.
Musa Arafat, a first cousin of the Palestinian leader, was appointed as the new head of public security. He replaced Abd Al-Razzaq al-Majaidah, who was moved to the role of security adviser on Saturday.
"The current changes are not a solution to the rampant corruption," said Abu Iyad, a spokesperson for the Janin Martyrs' Brigade.
"It's replacing a corrupt person with one that is even more corrupt. And this is a solution that cannot possibly satisfy any Palestinian, not just our brigade, because the Palestinian people are the ones who have suffered at their hands," he told Aljazeera.net on Saturday.
Asked whether there would be more kidnappings, Abu Iyad said his group would do whatever was necessary to force the Palestinian Authority to reform.
"We will not allow corruption to return ever again. The Palestinian street will assume responsibility for prosecuting the authority, and we count ourselves at the top of the list," he said.