In an interview with Reuters, Davutoglu also said Turkey was stepping up aid to an estimated 1.5 million people displaced in northern Iraq's Kurdish region after a rapid advance by Islamic State militants brought the violence closer to its borders.
Turkey, eager to re-establish itself as a powerhouse in a rapidly changing Middle East, is already sheltering more than a million refugees from the war in Syria and is playing a major role in the development of Iraqi Kurdistan.
Despite crumbling relations with Israel, it also hopes through its ties with the Palestinian authorities to play a part in brokering a long-term settlement in the Gaza Strip.
A humanitarian truce in Gaza, where half a million people have been displaced by a month of bloodshed, held for a second day on Wednesday but could be sustained only if basic needs such as power, water and healthcare were provided, Davutoglu said.
"Yesterday I spoke with (Palestinian) President Mahmoud Abbas and we want to get the injured people, thousands of them. They need urgent medical therapy, and we have already allocated places in our hospitals for them," he said.
"We are talking with both Egypt and Israel to have an air bridge to send humanitarian assistance ... If permission is given, our air ambulances will be carrying these passengers," Davutoglu said, adding there was "no limit" to the numbers of injured Palestinians Turkey was ready to treat.
Israel withdrew ground forces from the Gaza Strip on Tuesday morning and started a 72-hour Egyptian-brokered ceasefire with Hamas, which rules the coastal enclave.
Efforts to turn the ceasefire into a lasting truce could prove difficult, with the sides far apart on their central demands, and each rejecting the other's legitimacy. Hamas rejects Israel's existence and vows to destroy it, while Israel denounces Hamas as a terrorist group and eschews any ties.
"We hope that the talks in Cairo will be successful to achieve a sustainable ceasefire and we hope that the rights of Palestinian people will be respected in the coming days, months and years ... The only way to achieve this is to have a Palestinian state," Davutoglu said.
"(Peace) is achievable if the international community acts in an objective manner ... But if they give a signal that international law, rules and values should be respected by all but Israel is an exception ... then it is not achievable."
Pro-Palestinian sentiment runs high in mostly Sunni Muslim Turkey, and protesters have repeatedly taken to the streets in recent weeks to demonstrate against Israel's offensive in Gaza.
Prime Minister Tayyip Erdogan, campaigning for a presidential election on Sunday, has likened Israel's actions to those of Hitler and warned it would "drown in the blood it sheds".