The clashes broke out as militiamen loyal to the ruling party Hamas tried to break up protests by police and civil servants against unpaid wages.
The deadliest exchange broke out near the parliament building in the centre of Gaza City. Two teenagers were among four people killed while scores more were wounded.
Two members of security forces close to Fatah were also killed in separate exchanges with armed men from forces controlled by the Hamas-led interior ministry, police and medical sources said.
Clashes also broke out in the southern Gaza Strip's main town of Khan Yunis, leaving 23 people wounded, medical personnel said.
In the Palestinian political capital of Ramallah, hundreds of protestors stormed the government compound and set fire to the headquarters of the Hamas-led government.
The offices of Hamas ministers and MPs were also torched.
Bipartisan political reaction
Palestinian President Mahmud Abbas ordered security forces under his command to return to their barracks after the fighting with troops loyal to the Hamas-led interior ministry.
The ministry had deployed the troops after police loyal to President Abbas joined thousands of civil servants in a month-old strike in protest at the government's inability to pay their wages as a result of a Western aid freeze imposed after the Islamists took power.
Hamas Prime Minister, Ismail Haniya, also issued an appeal for calm and spoke with President Abbas to seek joint efforts to rein in the violence.
"I call for an end to provocations and for national unity to be protected," Prime Minister Haniya told reporters.
In his conversation with the president, Mr Haniya stressed the "need for the government and the presidency to work together ... to halt these tensions and ensure respect for law and order," a spokesman from his office said.
Those security personnel who had taken part in demonstrations needed to "respect the law and discipline and not take to the streets," he added.
It was the latest violence between Fatah and Hamas supporters in the territories, which have been gripped by a severe political and financial crisis since Hamas formed its government.
The two factions had been engaged in talks on forming a government of national unity acceptable to the Western donors but the violence appears to overshadow any hope of a breakthrough.