The Palestinian group, Hamas, says it's willing to agree to an offer of an Israeli ceasefire.
Israeli Defence Minister Ehud Barak made the ceasefire offer on Israeli public radio.
After a night of relative calm, both Israel and Hamas say they are ready for a truce if the other stops firing.
A Hamas spokesperson in Gaza says Palestinian factions did not want an escalation saying that if Israeli aggression stopped there would be calm.
At least 18 people have died in Israeli air strikes, which it says have been in response to militant rocket fire.