The Hamas-led Palestinian government is willing to urge militants to renew a ceasefire if Israel halts its attacks on Gaza, a spokesman has said.
Islamic Jihad said it was to blame for Thursday's rocket attack
Ghazi Hamad said the government would urge militant groups to stop firing rockets from Gaza into Israel.
The Islamic Jihad group says it was to blame for the latest attack on Israel.
Tensions have increased since the deaths of eight Palestinians on a beach, for which Israel has denied military responsibility.
Hamas ended an informal ceasefire last week amid escalating tensions following the beach killings on Friday.
Israel has said it was not responsible for the deaths near Beit Lahiya, but Palestinians have dismissed Israel's denial and are calling on the United Nations to hold an independent investigation.
Since the deaths, Hamas has fired dozens of home-made rockets at Israel, causing panic and several injuries.
But Mr Hamad told Israel Radio on Thursday he had spoken to Prime Minister Ismail Haniya, who had said the Palestinians wanted "quiet everywhere".
"We are interested in a ceasefire everywhere," Reuters news agency quoted Mr Hamad as saying.
"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."
Israel welcomed the offer, the Associated Press news agency reported, quoting foreign ministry spokesman Mark Regev as saying: "If it is quiet, we will answer that with quiet."
Israel frequently bombards northern Gaza, targeting militant rocket crews who attack nearby Israeli territory.
Earlier, Israeli officials said threats from Israel had stopped Hamas militants from firing rockets.
Israel regularly attacks northern Gaza, targeting Palestinian militants
A senior Israeli defence ministry official, Maj Gen Amos Gilad, told Israeli Army Radio on Thursday that attacks by Hamas had fallen after threats from Israeli officials.
"We sent clear messages... and at the end the firing of the rockets stopped," AP quoted him as saying.
Israeli media reports said Mr Haniya had asked his Hamas group's armed wing to stop the attacks, but Hamas officials denied this.
In other developments on Thursday, a second Palestinian minister crossed the border from Egypt into Gaza with a large amount of money in his luggage.
Information Minister Youssef Rizqa was carrying $2m (£1.6m), a day after Foreign Minister Mahmoud Zahhar returned to Gaza with $20m in his luggage.
Officials said the money would be used to pay workers' salaries. The Hamas-led Palestinian Authority has faced a financial crunch since Western donors cut off funding, accusing Hamas of being a terrorist group.