Palestinian factions have said there can be no truce if Israel keeps up its attacks and refuses to extend a ceasefire in the Gaza Strip to the West Bank.
But Abbas said the armed groups should take the first step, halt rocket fire for a month to allow for negotiations on a more comprehensive truce that would include the West Bank.
"Hamas is trying to draw us [Israel] into their civil war"
Zafon, Beersheva, Israel
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"Israel … can do what it wants, whenever it wants but we say we should do our duties and put the ball in the Israeli court," he said.
Israel's political and military leaders authorised the army to intensify ground operations against Palestinians in Gaza who have been firing rockets at Israeli border towns but officials said a major thrust into the coastal strip was not imminent.
Past large-scale offensives have failed to quell the rocket fire.
The green light to send more troops into Gaza was given on Monday by Ehud Olmert, the prime minister, a day after rockets claimed their second victim in less than a week in the southern town of Sderot.
Eight more rockets struck southern Israel on Monday, slightly injuring one person.
Israel has carried out about 60 air strikes, including one in the north of the Gaza Strip on a Hamas sports club late on Monday, injuring four Palestinians, including a woman and a child, Palestinian security sources said.
The air raids have killed about 50 Palestinians, including several military commanders, knocked out Hamas bases and pushed the movement's leadership underground in 12 days of air attacks.
Ismail Haniya, the prime minister, missed a cabinet meeting in Gaza City on Monday, citing security concerns.
Separately, Abbas's Fatah faction said on Monday it had accepted a proposal from Egypt to meet Hamas in Cairo next week to end factional fighting.
Hamas said it would also send delegates to Cairo.
Fatah and Hamas reached a truce a little over a week ago to stem fierce factional fighting that killed more than 50 Palestinians, but tension between the two groups remains high.
On Monday, Hamas and Fatah fighters traded fire over a stolen jeep in Shati before officials stepped in to calm tensions.
Meanwhile, Rafi Eitan, Israel's pensioners minister, suggested on Monday that a foreign peacekeeping force be deployed in and around Gaza.
He cited the boosted UN force in Lebanon after Israel's war against Hezbollah last year.
"The same thing, sooner or later, will happen in the Gaza Strip, with the senior partner in such a force being Egypt because it has no choice," Eitan told Israel Radio.
Israel has long resisted the peacekeeper idea but has signalled flexibility on the issue since the Lebanon war.
Olmert's spokeswoman said Eitan's thinking was not that of the government.