The unrest, the worst since Hamas trounced the former ruling Fatah in January’s election, broke out near the southern Gaza Strip town of Khan Yunis following a series of tit-for-tat kidnappings, police and witnesses said.
Two followers of Fatah and one Hamas activist, all in their 20s, were killed in the violence in the village of Abasan, according to hospital officials.
A local security official was injured and in a serious condition in hospital. The sources said at least one anti-tank rocket was fired.
Relations between the two groups have been strained for weeks, with about 30 people already injured in inter-faction clashes last month.
Despite ending Fatah’s longstanding grip on power, Hamas does not control the security services which are the responsibility of Palestinian Authority president and de facto Fatah leader Mahmud Abbas.
The overall leader of Hamas, the Damascus-based Khaled Meshaal, last month accused Abbas and Fatah of plotting against the movement which is under massive pressure after the West cut aid payments to the Palestinian Authority.
But in a bid to calm troubled waters, Mr Haniya said it was vital that followers of both factions exercise “self-restraint” and “preserve Palestinian blood” in the aftermath of the deadly violence.
“A civil war will never be allowed to be happen. We will fulfill our responsibilities in order to put an end to the tensions,” Mr Haniya told reporters before meeting with deputies in his office.
“The situation in Khan Yunis is now calm and I hope that it will remain that way. We are in contact with all the factions to ensure that these tensions dissipate.”
Witnesses said the clashes in Abasan erupted after Hamas members attempted on Sunday to seize Salman Abu Mutlak, head of security in the Gaza Strip.
A Fatah spokesman laid the full blame for the violence at the door of Hamas, saying two vehicles containing members of the security services and Fatah members had been attacked by Hamas gunmen.
“They opened fire with automatic weapons and with an anti-tank rocket,” Tawfiq Abu Khussa said.
“We hold Hamas fully responsible for these incidents which are part of a campaign of provocation against Fatah which is being led by Said Siam,” he added.
Hamas interior minister Siam last month announced the formation of a new volunteer security unit, a move which was swiftly vetoed by Abbas.
Hamas spokesman Sami Abu Zuhri however said the incident began after members of the preventive security force kidnapped three members of Hamas’s armed wing. They were later released after mediation between local faction leaders.
The latest clashes broke out during a visit to Hamas’s Gaza stronghold by Abbas which was aimed at defusing some of the tensions and seeking a common approach to steer the Palestinians out of their deep financial crisis.
Ministers from the Hamas-led government and aides to Abbas held a meeting on Sunday (local time) to discuss the situation but failed to reach agreement on how to address the crisis which has left government employees – including members of the security services – unpaid for the last two months.
“The participants did not agree on any of the points and so there will not be a follow-up meeting tonight between Mr Haniya and Abbas,” a source in Abbas’s office said, asking not to be named.