"We confirm the importance of Palestinian dialogue and we are ready to have this dialogue with Mr Abbas, but we reiterate that the armed resistance is connected to the existence of the occupation," Muhammad al-Hindi, leader of Islamic Jihad in its Gaza Strip stronghold, said.
"This armed resistance is in defence of the Palestinian people and in our dialogue we will confirm the importance of maintaining the resistance.
"It is the main method to prevent the incursions as happened today in Zaitun," he added in reference to the killing of four Palestinians in an eastern neighbhourhood of Gaza City on Saturday morning.
Meanwhile, Hamas said a ceasefire should only be considered if Israel ends its aggressions.
"We are an occupied nation which is defending itself," Hamas spokesman Sami Abu Zhuri said.
"The issue should be raised with the Israeli enemy only when they stop all kinds of aggression. The Palestinian people can then study this choice and decide whether it is in their interests."
On Friday, thousands of Palestinians marched in the streets of Jabalya refugee camp in the Gaza Strip in what they described as a victory march following a Thursday night attack which killed six Israelis at a vital crossing.
The march was organised by resistance groups and was seen as a sign of grassroots support for their defiance of Abbas and the battle against occupying Israel.
Resistance fighters march in
Three Palestinians were also killed during the bombing and shooting assault at al-Mintar (Karni), the main cargo crossing between Israel and Gaza, late on Thursday.
Three groups claimed they carried out the attack: Hamas, the Popular Resistance Committees and al-Aqsa Martyrs Brigades, an armed wing of Abbas' Fatah movement. Israel signalled it would weigh its response to the bombing carefully to avoid weakening Abbas.