"This people will remain united in the face of occupation and aggression and will not be derailed by internal struggles," he said during a televised address in Gaza City.
Palestinians fought outside Gaza's main hospital and the headquarters of the Fatah-controlled general intelligence agency came under mortar fire.
Nour Odeh, Al Jazeera's Gaza correspondent, said: "Clashes have become uglier, and exchanges have even taken place next to a hospital".
Most of the streets were empty and the shops were closed. Many parents in Gaza stopped sending their children to school after five students were wounded in the cross fire.
A total of 13 members of Hamas and Fatah were kidnapped in various incidents in the Gaza Strip.
"The smallest drop of Palestinian blood is dear to us and it should not be spilled except to defend our land," Haniya said.
The clashes between Hamas and Fatah supporters broke out after the Palestinian president and the head of Fatah, called at the weekend for early elections.
Haniya repeated his opposition to Abbas' plan and again accused him of planning a coup.
|Schoolgirls run past a Hamas fighter [AFP]|
"We consider the issue of the early elections for the presidency and parliament unconstitutional," he said.
"If you consider the people the source of power, why are you working against the will of the people?"
But Haniya also made conciliatory gestures to Abbas urging his interior minister to convene a meeting of rival security chiefs to discuss ways to calm the situation and reiterating a call for a long-term truce with Israel.
Hamas officials have proposed the truce, which Haniya said could last 20 years, before and it has been rejected by Israel.
The prime minister accused the United States of trying to topple the nine-month old Hamas government.
"There exists a non-declared decision to topple this government. This policy is being carried out by the Americans," he said.
Washington considers Hamas a terrorist organisation and refuses to deal with it until it accepts Western demands.
Mahmoud Abbas had earlier issued a statement calling for an end to the clashes, the fiercest of which took place in the centre of Gaza City and claimed the lives of two of his security forces.
"As president of the Palestinian people, I call on everybody to cease fire now ... to save our unity," he said.
"The agreement signed between the Palestinian factions should be applied on the ground, and Palestinian security forces should deploy in the streets in order to bring a halt to the actions of the combatants."