At least 32 Hamas supporters in Ramallah were wounded by gunfire from Mahmoud Abbas's forces on Friday, hospital officials said.
Several were in a critical condition.
As the fighting started in the West Bank, Hamas and Fatah forces in Gaza started exchanging fire on the streets.
Outside Ramallah's main mosque, Hamas supporters taunted Abbas's security forces, saying: "You look like Israeli soldiers. You are spies."
Güncelleme Tarihi: 20 Eylül 2018, 18:16
Dressed in riot gear, the Fatah-dominated forces used clubs and rifle-butts to beat back the Hamas demonstrators before shooting broke out.
The mosque was damaged.
Meanwhile, Khalil al-Hayya, the head of Hamas's faction in parliament, told 100,000 of the movement's supporters in Gaza City: "What a war Mahmoud Abbas you are launching, first against God, and then against Hamas."
The Palestinian president is expected to give a major speech around midday (1000 GMT) in Ramallah.Hayya did not say what Hamas would do if Abbas made such an announcement.
Ismail Haniya, the prime minister and leader of Hamas, was more conciliatory at the rally, appealing for "national unity", but stopping short of explicitly calling for calm as he had during previous spikes in internal fighting.
Tensions were at their highest in a decade and followed months of failed talks to form a unity government between the ruling Hamas Islamist faction and Abbas's once dominant Fatah.
Hayya said Hamas would not agree to holding an early election or a referendum on the issue, a move that Abbas could announce in a speech planned for Saturday in an attempt to break the political deadlock.
|Haniya "will choose ballots" to avoid civil war|
Al Jazeera has learnt that Abbas may seek expert opinion on the legality of calling early election.
"He is leaning towards calling for early elections," Saeb Erekat, a senior aide to Abbas, told Reuters.
"The president's choice is between bullets and ballots. He will choose ballots. Ballots are the only way to avoid the prospect of a civil war."
Some analysts question whether Abbas will make such a bold announcement with emotions running at fever pitch.
Ismail Rudwan, a Hamas spokesman, accused Mohammed Dahlan, a Fatah regional commander and legislator, of being behind the attack on Haniya's convoy in Rafah on Thursday.
Security forces fired on the prime minister's convoy after it had passed through the crossing. One bodyguard was killed and several other people injured. The bodyguard was buried in Gaza on Friday.
Dahlan rejected the allegation. He said it was part of a Hamas "cover-up" after unidentified fighters this week shot dead three young sons of an intelligence official loyal to Abbas outside their school.
Haniya has condemned the killings and the government said on Friday it would investigate the incident.
Erekat, at a news conference, strongly condemned the accusation against Dahlan, saying it amounted to an official sanction for the Fatah politician's assassination.