Ban said strong ties between Turkey and Israel, which both share a border with Syria, were important for the middle East.
United Nations Secretary-General Ban Ki-moon urged Turkey and Israel on Saturday to improve their relationship and accept the recommendations of a U.N. report into the deaths of nine Turks in Israeli attack on a Gaza-bound ship.
Realtions between Turkey and Israel have deteriorated since the U.N. report was made public on Thursday. Turkey has expelled Israel's ambassador and frozen military cooperation after the report failed to prompt an apology from Israel.
Ban said strong ties between Turkey and Israel, which both share a border with Syria, were important for the middle East and the future of the Middle East peace process.
"I sincerely hope that Israel and Turkey will improve their relationship," Ban told reporters in Canberra after talks with Australian Prime Minister Julia Gillard.
"Both countries are very important countries in the region. Their improved relationship, normal relationship, will be very important in addressing all the situations in the Middle East, including the middle east peace process.
Ban said he would make no comment on the specifics of the report, written by a panel headed by former New Zealand Prime Minister Geoffrey Palmer.
"My only wish is that they should try to improve their relationship and do whatever they can to implement the recommendations and findings of this panel's report," he said.
The report found Israel's naval blockade of the Gaza Strip was legal, but that Israel used unreasonable force when its commandos raided the ship, despite meeting strong resistance from those on board.
The rift between Turkey and Israel comes despite U.S. efforts to encourage a rapprochement between two regional powers whose cooperation it needs to address changes sweeping the Middle East.
Ban is in Australia on his way to the Pacific island nations of Solomon Islands and Kiribati. He will also attend a meeting of Pacific Islands leaders in New Zealand, where he will discuss the threats of climate change.