US President George W Bush has demanded that the Palestinian leadership must stop attacks against Israel, a day after two suicide bombings killed 15 people.
Gunmen were out in force at the funeral of victims of the Gaza raid
Mr Bush said "time would tell" if the US could work together with the new Palestinian Prime Minister Ahmed Qurei, who confirmed he had accepted the post on Wednesday.
Despite the bloodshed, Mr Bush insisted the roadmap peace plan was still in place.
Israeli missiles earlier targeted the home of a senior member of the militant group Hamas, Mahmoud Zahar, killing his son and a bodyguard and injuring 25 people.
"I still believe strongly that the two states living side by side in peace is a hopeful vision for the future of the Middle East. The roadmap is still there," Mr Bush said.
But he urged Mr Qurei, widely known as Abu Ala, to take action against militant networks.
"His job, if he's interested in a two-state solution, is to consolidate power within his administration, to get the security forces under control, all the security forces, and then unleash those security forces against the killers," he said.
Mahmoud Abbas stepped down as prime minister at the weekend over a struggle with President Yasser Arafat for control of the security forces.
Mr Bush also said Israel had a responsibility "to create the conditions necessary for those in the Palestinian Authority who do believe in peace... to prevail".
Israel in shock
The air strike against Mr Zahar prompted the military wing of Hamas to threaten to attack "houses and tower blocks" in Israel in retaliation.
The latest Israeli strike caused extensive damage to a mosque, and left huge plumes of smoke rising from Mr Zahar's neighbourhood. Correspondents say he has now gone into hiding.
The raid on Gaza City was condemned as "cowardly" by Mr Qurei.
Israel was stunned by Tuesday's two suicide attacks, which killed 15 Israelis.
The military wing of Hamas on Wednesday claimed responsibility for the twin bombings, describing them as revenge for Israeli attacks.
Hours after a suicide bomber set off explosives at a crowded bus stop near Tel Aviv, another bomber detonated a device outside a cafe in Jerusalem.
The first bombing took place outside Tsrifin army base, in the Tel Aviv suburb of Rishon Letsion, killing eight people waiting at a bus stop and injuring around 30.
The second suicide bombing was in the heart of west Jerusalem, at the crowded Cafe Hillel, on one of the liveliest streets in the city.
Seven people as well as the bomber are believed to have died in that attack and about 30 were wounded.
The violence caused Israeli Prime Minister to cut short a visit to India.