Abbas had travelled to Gaza on Tuesday for talks with resistance groups to urge them to halt rocket attacks on Israeli towns.
Saeb Erikat, a top Palestinian negotiator and participant in the meeting, said Abbas urged all Palestinian groups to honour a
ceasefire reached with Israel in February.
"We demand everyone be committed to the truce," Erikat said. "We consider the truce of high national interest."
But Islamic Jihad, which has been responsible for most of the rocket fire, rejected the appeal.
Khalid Batch, a Jihad spokesman, accused Israel of violating the ceasefire, and said attacks were the only proper response.
"I think the continuation of resistance is what's better for the
Khalid Batch, spokesman,
"I think the continuation of resistance is what's better for the Palestinian people," he said.
Since Israel's withdrawal from the Gaza Strip in September, resistance fighters have continued to fire rockets into southern Israel.
With Israel out of the area, more Israeli towns have come into rocket range.
Last week, a rocket landed near Ashkelon's power plant and a fuel depot.
Israeli jets have launched strikes
in response to rocket attacks
Israel has responded with air strikes on suspected launch sites in northern Gaza and threatened to impose an off-limits zone near the border with Israel.
The Israeli air force has dropped leaflets into northern Gaza, warning residents to stay out of areas used by fighters to fire rockets.
"Presence in areas used for projectile rocket launching puts your life in danger," the leaflets said.
Abbas' ability to rein in the resistance groups - already in doubt due to lawlessness in the Palestinian territories - was dealt a further blow on Tuesday.
Al-Aqsa Martyrs Brigades fighters - part of the Fatah movement led by Abbas - took over a West Bank office of the Palestinian election commission to protest against his choice of candidates for an upcoming parliamentary election.
The fighters said they seized the al-Ram office to demand the
inclusion of candidates representing neighbouring Jerusalem on the list of those contesting the 25 January vote.
Abbas has tried to merge rival lists within Fatah, which has threatened to undercut the movement's chances against Islamic resistance group Hamas at the ballot box.
Brigades fighters protesting at
Abbas' choice of poll candidates
Fatah is struggling to cope with a split between veterans from a corruption-tainted old guard and younger members seeking a bigger share of influence.
Ammar Dwaik, a senior election official, said: "We are very annoyed. Fatah should solve their internal differences outside our offices."
In the West Bank city of Bethlehem, 400 people, including members of the Brigades, held a protest outside Fatah's main office dissatisfied with the candidate list.
Armed men fired in the air while tyres were burned and demonstrators urged Abbas to reconsider the line-up of those
standing for election.
Abbas needs to submit the new list on Wednesday, when party registration for the election will reopen for a few hours.
But Fatah officials said it remained unclear whether a unified Fatah list could be finalised by Wednesday.
Israel said on Monday it was considering allowing East Jerusalem residents to vote in the election and dropping a threatened ban that drew calls for the ballot to be postponed.