Abbas condemned the killings in Tulkarm, saying they undermined the peace process and a truce observed by Palestinian factions.
"At a time when the Palestinian Authority is trying to maintain calm, this murder intentionally aims at renewing the vicious cycle of violence," Abbas said in a statement on Thursday.
But Abbas also urged the Palestinians "not to respond to such provocations by the Israeli government, so as not to give Israel a pretext to escalate its aggression".
The five fighters, one from Islamic Jihad and the rest from al-Aqsa Martyrs Brigades, were shot and killed when an arrest operation in Tulkarm refugee camp disintegrated into a shootout.
The shootings on Thursday, Israel's first deadly operation since the pullout of settlers from Gaza, came as a British Jew was stabbed to death by a lone Arab in the first fatal Palestinian attack in Jerusalem's Old City in three years.
The bloodshed and plans to build a major new Israeli police station in the occupied West Bank deflated international optimism that the evacuation of Jewish settlers from Gaza would help revive the stagnant Middle East peace process.
Aljazeera correspondent in Tulkarim Muein Shadid reported that the Israeli occupation troops entered Tulkarim in a civilian car which bore Palestinian registration plates that appeared to be fabricated.
The troops immediately opened fire on a group of Palestinian citizens, among them were five who were fighters, as alleged by the occupation forces.
"At a time when the Palestinian Authority is trying to maintain calm, this murder intentionally aims at renewing the vicious cycle of violence"
One of them Ribhi Amara was a leader of the Izz al-Din al-Qassam brigades, the military wing of Hamas in Tulkarim. He escaped unharmed.
The Israeli occupation forces then opened fire at pointblank range at another group of Palestinian citizens including youngsters, killing five people.
Eyewitnesses said the Israeli force could have arrested the Palestinians, since they were unarmed.
Three other Palestinians were wounded and taken to hospital for treatment, Shadid reported.
The Israeli army said all five were from Islamic Jihad and were wanted in connection with a bombing last month that had killed five Israelis, which was claimed by the group.
The killings of the fighters provoked predictable vows of revenge from resistance groups.
"The enemy should prepare the coffins for their soldiers and settlers because the revenge will be swift and deep inside Israel," Islamic Jihad said in a statement.
"Our revenge will be very quick and like an earthquake against this massacre," al-Aqsa Martyrs' Brigade added.
Gaza-based resistance groups fired two makeshift rockets into southern Israel on Thursday in the first such attack since Israel evacuated all its settlers from the territory it has occupied for four decades. There were no injuries.
Islamic Jihad vowed a quick
revenge deep inside Israel
Violence also struck in Jerusalem's Old City where a young Jewish seminary student from London was stabbed to death by a Palestinian near Jaffa Gate.
His American classmate was also injured by the attacker who fled from the scene.
The international community has warned Israel that the Gaza withdrawal can only be a beginning, and pushed for a resumption of talks on the Mideast peace road map.
But on Thursday, Israel announced plans for building a new police headquarters on public land east of Jerusalem, just outside Maale Adumim, the largest West Bank settlement.
"The construction project for a police HQ and an access road has obtained all the necessary authorisations and will begin shortly," a military spokesman said.
Israeli Prime Minister Ariel Sharon has frequently said that after the Gaza pullout Israel will expand its settlement activity in the West Bank.
In March, Israel drew international condemnation by announcing plans to build 3500 houses in Maale Adumim.
The move will in effect cut off the West Bank from occupied east Jerusalem.
Palestinian Prime Minister Ahmed Qorei called Israeli plans for the Jerusalem area "very dangerous".
"No one who is interested in peace can accept this and there must be very rapid moves from the international community because it has more significance than what Israel has been doing in Gaza."