Clashes on Sunday in the Gaza Strip and the West Bank left eight people dead and more than 100 wounded.
Ismail Haniya made his plea as Israeli tanks, bulldozers and troops moved into northern Gaza on Sunday evening. The Israeli army had said the operation was to stop rockets being fired into Israel.
Haniya said: "As prime minister, I call on all citizens to show responsibility and to be above disagreements, especially in the face of a serious escalation from the occupation forces, which is threatening to expand the aggression on Gaza."
In the latest round of violence one Palestinian protester was killed and several dozen were injured.
Earlier in the day seven people died and at least 50 were injured in gun battles between rival Palestinian security forces in the Gaza Strip.
Forces controlled by the Hamas-led government clashed with loyalists of Abbas's Fatah movement, as tensions rose over unpaid wages.
Said Siyam, the interior minister and a Hamas member, deployed his security forces to prevent further violence by striking police.
The police, loyal to Abbas, blocked Gaza's roads with burning tyres and demanded overdue salaries.
One resident, Majed Badawi, 33, whose car was caught in the crossfire, said: "This is forbidden in Islam, we are in the holy month of Ramadan.
"It's a shame on Hamas, who call themselves real Muslims, and a shame of Fatah as well. Why are they fighting and over what? We are victims because of both of them."
Abbas urged "all members of the security forces ... not to participate in the demonstrations against the delayed payment of wages," according to a statement from his Ram Allah office.
The cabinet building in the West Bank city of Ram Allah was stormed by supporters of Mahmoud Abbas, the Palestinian president, following the gun battles.
A room was set on fire in the empty building. No injuries were reported.
Presidential building attacked
In Gaza City, Hamas loyalists took to the roof of the agriculture ministry and fired rocket-propelled grenades and machine guns at the presidential guard, killing one.
Islam Shawhan, a spokesman for the Izz al-Din al-Qassam Brigades, Hamas's armed wing, said: "We are going to beat with iron fists all those elements who are trying to sabotage the election process of our people, those who are trying to destroy our public properties and close the streets.
"We are not going to hesitate to take action against any of them."
A fire was started inside the
Tawfik Abu Khoussa, a Fatah spokesman, said: "Nothing can justify this violence."
Ghazi Hamad, a government spokesman, said the violence was "regrettable," but that the Hamas force acted with restraint and was attacked by demonstrators.
Abbas has been locked in a power struggle with the Hamas-led government which defeated Fatah in parliamentary elections in January.
Most civil servants have been on a protest strike since September 2, with more than 160,000 Palestinian Authority (PA) employees awaiting full payment of salaries.
An aid embargo has prevented the PA from paying full salaries to civil servants for more than six months, including the security services, though some wages have been paid in recent weeks.
The ability of the PA to pay wages has also been restricted due to Israel withholding customs duties and value-added taxes due to the Palestinians.
Such monies are usually distributed to the PA via Israeli channels, as per the terms of the 1993 Oslo Accord.
Israel has abrogated the accord in a bid to limit the influence of Hamas, which does not recognise Israel.