Clashes have erupted between rival Palestinian factions after Hamas accused Fatah of trying to assassinate Prime Minister Ismail Haniya of Hamas.
Security forces loyal to Fatah clashed with Hamas in Ramallah
Hamas accused a senior Fatah figure of organising an attack on Mr Haniya as he crossed into Gaza from Egypt.
Medical sources in the West Bank town of Ramallah said 32 people had been injured in clashes there. Fighting was also reported in Gaza City.
Mr Haniya called for calm and unity at a mass rally held in Gaza City.
Tens of thousands of supporters gathered in a Gaza City football stadium to mark the 19th anniversary of the founding of Hamas.
Hamas gunmen patrolled the streets of the city in a show of strength.
Mr Haniya said Hamas had the names of those responsible and that the law would be used to bring them to justice.
But he vowed that the shooting would not frighten members of Hamas.
"We did not join this movement to become ministers but rather to become martyrs."
One bodyguard was killed and Mr Haniya's son was among five injured in Thursday's gun battle at the Rafah border crossing.
The BBC's Alan Johnston, in Gaza, says Mr Haniya struck a less strident tone than some, but there is every danger that the situation could get worse.
Mahmoud Abbas, the Palestinian Authority (PA) president and head of Fatah, is due to speak on Saturday, and may call early elections in an effort to break the political deadlock between Fatah and Hamas.
Hamas has said it will boycott Mr Abbas' speech in protest at "dangerous and bloody" recent events.
Egyptian negotiators, who have mediated between Hamas and Fatah in the past, met Hamas on Friday in an effort to ease tensions.
Russia also called for the quarrelling factions to show restraint.
The violence in Ramallah on Friday flared as Hamas supporters attempted to march towards the centre of town but found the path blocked by Mr Abbas' security forces, reports said.
Fighting broke out, with hospital officials saying that at least 32 people were injured by gunfire and stone-throwing.
Shooting also erupted in Gaza City between masked Hamas gunmen and PA police allied to Fatah.
A Hamas spokesman had earlier said the Rafah attack was "an assassination attempt carried out by traitors led by Mohammad Dahlan".
Mr Dahlan, an ally of Mr Abbas, is a former Palestinian Authority security chief and a fierce critic of Hamas.
He rejected the Hamas accusations, saying the governing party was trying to "mask its failures".
A Fatah spokesman said the attack was a "grave threat" to Palestinian unity.
Inter-faction tensions have increased since the killing of three sons of a pro-Fatah security chief on Monday.
Mr Haniya had tried to cut short his first trip abroad as prime minister to deal with the crisis.
But Israel on Thursday closed the Gaza border, saying the reported $30m (£15.3m) Mr Haniya was carrying in donations as he returned from his foreign trip would fund "terrorist operations".
When Mr Haniya eventually crossed late in the evening, without the money, guards allied to Fatah exchanged fire with Mr Haniya's security forces.
Hamas, a militant Islamic group, won elections in January, but has faced a Western aid boycott after refusing to renounce violence and recognise Israel.