A top commander of the Palestinian security forces said after Tuesday night's meeting that forces would be deployed along the Gaza Strip's borders with Israel within days to enforce Abbas' order to halt attacks.
Public security chief Major-General Abd al-Razik al-Majaydah said an "arrangement is under way to deploy national security forces on the borders within two days to prevent violations".
Abbas arrived in Gaza City on a mission to persuade Palestinian resistance groups to lay down their arms with a view to revive peace talks with Israel.
"Calm was one of the points raised in the meeting within the framework of stabilising the Palestinian situation," said Sami Abu Zuhri, a Hamas spokesman in Gaza. "We have listened to Abu Mazin and we will study the issue within the movement."
He said further meetings were expected.
Bomb at checkpoint
Hamas claimed responsibility for Tuesday's attack by a 21-year-old bomber, who detonated his explosives during an identity check by Israeli security personnel.
An agent of Israel's Shin Beth security service was killed, and seven other Israelis and two Palestinians wounded.
The military wing of the Hamas resistance movement, the Izz al-Din al-Qassam Brigades, said it carried out the attack and identified the Palestinian who blew himself up as Umar Sulayman Tabash from Absan village, near Khan Yunus.
Witnesses were quoted as saying the bomber approached a group of people at an al-Matahin road intersection and blew himself up.
Brigades halt attacks
In the West Bank, a leader of al-Aqsa Martyrs Brigades pledged to halt attacks inside Israel but said it would continue to strike at Israelis in the occupied West Bank and Gaza.
"We agree to suspend all military action inside Israel ... in order to support Abbas' political programme," said Zachariya Zubaidi.
Settlements built on occupied Palestinian territories are illegal under international law.
Israeli Prime Minister Ariel Sharon meanwhile visited troops in the northern Gaza Strip. His office said he discussed how to stop rocket and mortar fire at Jewish settlements.