Israel says it is willing to observe a ceasefire after days of military exchanges in Gaza, if Palestinian militants there end rocket attacks.
Israeli Defence Minister Ehud Barak said on Sunday: "If they stop firing on our communities, we will stop firing."
A spokesman for Hamas, which runs Gaza, said militants were not interested in escalation and calm could be restored.
At least 18 people have died in Israeli air strikes, which it says have been in response to militant rocket fire.
Mr Barak made the ceasefire offer on Israeli public radio, saying: "If they stop firing in general, it will be quiet, it will be good."
But he added: "We cannot tolerate firing... We will act along the lines of what happens on the ground."
Prime Minister Benjamin Netanyahu later told Israeli radio that "if the criminal attacks against Israeli military and civilians continues, Israeli will respond with even more force".
Hamas spokesman Sami Abu Zuhri told the Reuters news agency: "If the Israeli aggression stopped, it would be natural for calm to be restored. Calm will be met with calm."
Although three mortar shells were fired by Palestinian militants overnight this was a sharp drop from previous days.
'Crossed the line'
The latest round of violence followed a Hamas anti-tank rocket attack on a school bus near the Nahal Oz kibbutz last week.
A 16-year-old boy suffered serious injuries and the driver was also wounded.
Several civilians were among those killed in the following Israeli air strikes. Dozens of people have been wounded.
Israel's strikes and the dozens of rockets and mortars subsequently fired by militants across the border represent the worst violence in Gaza in two years.
The violence led Mr Barak to postpone indefinitely a trip to Washington.
Israel has previously taken a hard line on the exchanges of fire.
Mr Netanyahu said the bus attack had "crossed the line", adding: "Whoever tries to hurt and murder children, his blood will be on his own head."
On Saturday, a senior Israeli security official told Agence France-Presse that Hamas's political branch had sent a message asking for a truce.
Hamas declared a state of emergency in Gaza on Saturday following the Israeli air strikes.
