Palestinian militant groups Hamas and Islamic Jihad say they will maintain an undeclared truce while they consider joining a ceasefire with Israel.
Hamas received the Palestinian leader in its Gaza heartland
Senior Hamas leader Mahmoud Zahar said the group would make a final decision after reflecting on Saturday's talks with Palestinian leader Mahmoud Abbas.
Islamic Jihad confirmed it would also respect the undeclared peace.
Mr Abbas went to Gaza hoping to sell the full ceasefire that he agreed with Israel on Tuesday to the groups.
Mr Zahar said that in certain circumstances, Hamas would consult Mr Abbas's administration on what he called "the mechanism for the retaliation".
Any suggestion that Hamas might consult with the Palestinian Authority on any aspect of its military activity would be something entirely new, the BBC's Alan Johnston reports from Gaza City.
This would be taken as an indication that Mr Abbas had made some important progress in these talks, he adds.
The Palestinian leader was thought to have argued that the agreement with Israel does meet most of the groups' demands regarding a cessation of Israeli military activity.
In another development, Israel agreed to hand control of the West Bank town of Jericho to the Palestinian Authority as early as mid-week.
The talks came hours after Israel agreed to allow the return of up to 60 Palestinians expelled from the West Bank in 2002.
A Hamas attack on Thursday briefly put the truce under question
The men, accused by Israel of terrorist involvement, include 40 Palestinians who took part in a month-long siege in Bethlehem's Church of the Nativity.
But Hamas is concerned that the release will not be nearly as sweeping as it wants and the group could be hard to convince, our correspondent says.
The militant organisation is also said to be worried that Mr Abbas might allow the process of talks with Israel to become bogged down in protracted negotiations that produce little for the Palestinians.
Mr Zahar said the group was waiting to see how Israel would act and wanted to be sure that Israel had stopped military operations and "targeted assassinations", and had made clear its criteria for freeing Palestinian prisoners
Tension grew on Friday after Hamas fired rockets and mortars at Jewish settlements, claiming retaliation for the death of a Palestinian man who was killed by army fire the day before.
However, Mr Abbas sacked some of his top security officials for failing to halt the attacks, Israel did not make any military response and the truce appeared to be still holding otherwise.
Islamic Jihad leader Mohammed al-Hindi warned on Saturday that the groups were under "heavy pressure" to resume hostilities.
"Israel has continued provocations against the Palestinian people and no one is blaming it," he told Arabic TV channel al-Jazeera.
Mr Hindi called for a "programme that would help us avoid these pressures".