"Turkey has conveyed a solid proposal to relevant sides (in Gaza) that will help establish a joint platform," he told broadcaster NTV in an interview on Friday. He did not elaborate the details of the offer.
Hurriyet daily, however, said the proposal includes the formation of an "international monitoring force" under Turkey leadership to ensure a sustainable truce if an immediate ceasefire is agreed.
Turkey also said the blockade on Gaza should be lifted and the humanitarian aids to the region would be allowed immediately, sources told Hurriyet.
The tunnels between Gaza and Egypt, which Israel says used to supply arms to Hamas militants, would be secured, the sources added.
Israel had launched air offensive in Gaza on Dec 27 and then a ground operation which left more than 1,100 Palestinians killed.
COMMUNICATION CHANNELS TO REMAIN OPEN
Although the Turkish government felt offended by the Israeli attacks, it has no plans to cut the ties with Israel.
"Mediation is a relationship of confidence... We pay high attention to keeping the channels of communication open. If the problems is to be resolved this will happen through dialogue,"
Babacan was quoted as telling NTV by the state-run Anatolian Agency.
"There must be mutual agreement among all sides in order to make a cease-fire permanent and sustainable," Babacan also said.
Cutting ties with Israel "in order to satisfy certain circles or in the name of populism will harm the region," he added
The minister admitted that Turkey had "a different tone of speaking (to Israel) when compared to the past, but this does not mean alienation or a decrease in our efficiency."
Iran and Syria have called on all countries to sever their ties with Israel. Qatar and Mauritania decided Friday to "suspend" their relations with the Jewish state.
Turkey has been active in mediation efforts to end the war and a Turkish delegation has shuttled between Cairo, where most talks took place, and Syria, where exiled Hamas leaders are based.