Speaking in Canberra, the United Nations Secretary-General told reporters "I sincerely hope that Israel and Turkey will improve their relationship", after Turkey expelled Israel's ambassador to Ankara and suspended all military ties with its one-time ally.
"Both countries are very important countries in the region and their improving relationship, normal relationship, will be very important in addressing all the situations in the Middle East, including the Middle East peace process."
The UN leader said he had been trying to help the countries improve their relationship since 31 May, 2010 when Israeli troops boarded a Gaza aid flotilla, leading to the deaths of nine people including eight Turks.
Turkey pulled its ambassador out of Tel Aviv in the immediate aftermath of the raid but on Friday Foreign Minister Ahmet Davutoglu announced that diplomatic ties would be further downgraded after a UN probe slammed the "excessive" force used in the raid, for which Israel has failed to apologise.
"The time has come for Israel to pay a price for its illegal actions. This price, first of all, is being deprived of Turkey's friendship," he said.
"All officials above the level of second secretary, primarily the ambassador, will turn back to their country at the latest on Wednesday," he added.
"Second, all the military agreements between Israel and Turkey are suspended."
The Turkish measures came after a leaked copy of the UN-mandated report criticised Israeli troops for using "excessive" and "unreasonable" force when boarding the ferry Mavi Marmara on 31 May, 2010.
"Israel's decision to board the vessels with such substantial force at a great distance from the blockade zone and with no final warning immediately prior to the boarding was excessive and unreasonable," said the inquiry, led by former New Zealand prime minister Geoffrey Palmer.
It added, however, that the flotilla "acted recklessly in attempting to breach the naval blockade" and the Israeli forces "faced significant, organized and violent resistance from a group of passengers".
The report's release has been delayed several times because of the failure of Turkey and Israel to agree a final version. It was finally handed to UN chief Ban on Friday.
Davutoglu said Turkish and Israeli officials held four rounds of talks to reconcile their differences and reached a consensus on two draft texts, which were also approved by Israeli Prime Minister Benjamin Netanyahu. But the agreements failed due to a split in the Israeli cabinet, he added.
Turkey has repeatedly said relations will not return to normal unless Israel apologises and compensates the victims, which it refused to do.
"Israel once again expresses its regret for the loss of human life but does not apologise for this operation," Netanyahu's office said in a statement on Friday.
"Israel, like every other country, has the legitimate right to defend itself," it added.
In a further reflection of the diplomatic meltdown, another senior official was quoted by Israeli public radio as saying that "relations between the two countries have been set back by years".
The US similarly urged Israel and Turkey to mend fences. The United States "has longstanding friendships with both Israel and Turkey," said State Department spokeswoman Victoria Nuland, adding: "We regret that prior to the publication of the report they were unable to reach agreement on steps that might have helped overcome their differences."
Washington, she said, hoped the two countries "will continue to look for opportunities to improve their longstanding relationship, and we will encourage both to work towards that end." Turkey had been Israel's closest ally in the Muslim world, holding regular joint military exercises, but ties had been going steadily downhill since Prime Minister Recep Tayyip Erdogan and his Islamist-rooted Justice and Development Party came to power in 2002.
They went into crisis when eight Turkish nationals and an American of Turkish descent died on the Mavi Marmara, the lead ship of the six-vessel convoy, after Israeli special forces in speed boats and dropped from helicopters boarded it in international waters.
The UN inquiry called on Israel to make "an appropriate statement of regret" and pay compensation to the families of the dead.
The United States meanwhile urged Israel and Turkey on Friday to mend fences.
The United States "has longstanding friendships with both Israel and Turkey", said State Department spokeswoman Victoria Nuland, urging the two sides "to look for opportunities to improve their longstanding relationship".