The Hamas government wants a ceasefire with Israel and is willing to ask Palestinian militants to stop firing rockets from Gaza, a spokesman said today.
But Ghazi Hamad said Israel had to first stop military activity in the Gaza Strip and the West Bank.
The Islamic militant group scrapped a 16-month truce with Israel last Friday and soon after launched a barrage of makeshift rockets at the Jewish state from Gaza.
"I spoke today with the prime minister and he said we definitely want quiet everywhere. We are interested in a ceasefire everywhere," Mr Hamad, speaking in Hebrew, said in an interview on Israel Radio.
Mr Hamad later said the offer was conditional.
"We are ready to launch discussions with factions over stopping rocket firing but only if there is an Israeli commitment to cease all military attacks against all Palestinians in Gaza and the West Bank."
Mr Hamad's remarks followed a sharp drop in militant rocket fire from the Gaza Strip.
Earlier this week a senior member of Israeli Prime Minister Ehud Olmert's party threatened Prime Minister Ismail Haniyeh of Hamas with assassination if the group resumed suicide bombings.
Israeli officials were not available to comment, but the Jewish state regards Hamas as a terrorist organization and along with the United States and the European Union has imposed an economic embargo on the new government.
Hamas is sworn to destroy Israel and has rejected Western demands to recognize it, disarm and accept past peace accords.
Army Radio reported four rockets hit the Israeli town of Sderot, near Gaza, on Thursday. That compares to 30 to 40 rockets launched daily just after Hamas ended its truce.
Medics said two people were lightly wounded in the latest rocket attacks, which were claimed by the Islamic Jihad group.
At an intersection near a Jewish settlement in the occupied West Bank, three Palestinians tried to force two young Israeli women hitchhikers into their car at gunpoint, slightly injuring one of them, the army said, calling it a kidnapping attempt.
Both managed to elude capture and the men sped off after an army officer driving by noticed the commotion. He gave chase and the car was stopped at a roadblock, where soldiers found a loaded pistol and arrested the three Palestinians, a local commander told reporters.
Many Jewish settlers hitchhike in the West Bank, seeking rides from fellow settlers, despite regular warnings by Israeli authorities of the risk of kidnapping by Palestinian militants.