Turkey has for the first time threatened to break diplomatic ties with Israel over its raid on a Gaza-bound aid flotilla in May.
Turkey's foreign minister said a break could only be averted if Israel either apologised or accepted the outcome of an international inquiry into the raid.
The Israeli government said it had nothing to apologise for.
Ankara curtailed diplomatic relations with Israel after the naval raid, in which nine Turks were killed.
Turkey - which until recently was Israel's most important Muslim ally - withdrew its ambassador and demanded that the Israelis issue an apology, agree to a United Nations inquiry and compensate the victims' families.
A Turkish foreign ministry official told the BBC relations with Israel had hit rock bottom, but Ankara would not rush into cutting ties.
Foreign Minister Ahmet Davutoglu said Turkey would be satisfied with the ongoing Israeli inquiry if that found Israel to be at fault.
Mr Davutoglu told Hurriyet newspaper: "[The Israelis] will either apologise or acknowledge an international, impartial inquiry and its conclusion. Otherwise, our diplomatic ties will be cut off."
He also said there was now a blanket ban in place on all Israeli military aircraft using Turkish airspace, not just on a case-by-case basis.
It comes just five days after a surprise meeting between Mr Davutoglu and Israeli Trade Minister Benjamin Ben Eliezer in Switzerland.
Reacting to the Turkish stance, Israeli Foreign Minister Avigdor Lieberman said: "We don't have any intention to apologise."
Foreign ministry spokesman Yigal Palmor told AFP news agency: "When you want want an apology, you don't use threats or ultimatums."
Israel says its commandos acted in self-defence after being attacked by activists wielding clubs and knives as the troops boarded one of the aid convoy ships.
Activists on board the Mavi Marmara say lethal force was used from the start of the raid by Israeli forces.
The vessel was part of a flotilla trying to break Israel's blockade of the Gaza Strip.
Amid mounting international pressure following the raid, Israel last month announced it would ease its four-year blockade of the territory.
On Monday, Israel published a revamped blacklist of items barred from entry into the Gaza Strip.
Long-standing restrictions on allowing consumer goods into Gaza are being dropped.
Construction materials, badly needed in Gaza, will only be permitted in under supervision for use by organisations such as the UN.
The Islamist group Hamas, which controls Gaza, said the measures were "worthless" and of no use to the Palestinians living there.
Israel says its blockade is needed to prevent the supply of weapons to Hamas.
Turkey and Israel forged strong military and trade ties following Ankara's recognition of Israel in 1949.
But relations have cooled in recent years. The Turkish government headed by the AK Party - which has Islamist roots - strongly criticised the raid launched by Israel in Gaza in December 2008.
In January 2009, Turkish Prime Minister Recep Tayyip Erdogan stormed out of the World Economic Forum in Davos, after a clash with Israeli President Shimon Peres.
In January this year, Israel was forced to apologise over the way its deputy foreign minister treated the Turkish ambassador.