Abbas made the request during a meeting late Tuesday with representatives of militant groups, including Islamic Jihad, the group behind most of the recent rocket fire.
Palestinian negotiator Saeb Erekat, a participant in the meeting, said Abbas urged all Palestinian groups to honor a cease-fire reached with Israel in February. "We demand everyone be committed to the truce," Erekat said. "We consider the truce of high national interest."
But the Islamic Jihad militant group on Tuesday rejected a call from Palestinian leader Mahmoud Abbas to halt its rocket attacks on Israel.
Islamic Jihad spokesman Khaled Batch accused Israel of violating a cease-fire agreement, and said attacks were the only proper response.
"The truce is in place, but there are Israeli violations," he said. "I think that the continuation of resistance is what's better for the Palestinian people."
Since Israel's withdrawal last summer from the Gaza Strip, militants have continued to fire rockets into southern Israel. With Israel out of the area, more Israeli towns, including the city of Ashkelon, have come into rocket range. Last week, a rocket landed near Ashkelon's power plant and a fuel depot, alarming Israelis.
Israel has responded with airstrikes on suspected launch sites in northern Gaza and threatened to impose an off-limits zone near the border with Israel.
Late Wednesday, the Israeli air force dropped leaflets into northern Gaza, warning residents to stay out of areas used by militants to fire rockets.
"Terror organizations continue to launch projectile rockets at Israeli territory from your neighborhoods," the leaflet said.
"Presence in areas used for projectile rocket launching puts your life in danger."
The Palestinian election comes amid a backdrop of growing violence with Israel and continuing chaos in the Palestinian territories.
Israeli aircraft on Tuesday fired missiles on two offices of a Palestinian militant group and attacked an overpass in the northern Gaza Strip, its latest response to a new wave of Palestinian rocket attacks. No injuries were reported.
The pre-dawn aerial strikes were part of the army's attempt to halt rocket fire on Israeli towns bordering Gaza.
Prime Minister Ariel Sharon has approved a buffer zone in northern Gaza, although the army said it has not yet implemented the plan — which includes firing on anyone who enters the area.