Asked whether Turkey would bring its diplomatic representation down to the level of charge d'affaires if it did not recieve an adequate response, Gul said: "We will make an evaluation after consultations with the ambassador."
The row comes ahead of a planned visit by Ehud Barak, the Israeli defence minister, to Turkey on Sunday.
On Tuesday, Turkey demanded "an explanation and apology" over the incident, which Celikkol described as a "mise en scene," saying he was led to believe he had been invited for introductory talks and not a protest.
"We expect an explanation and apologies from Israeli authorities for the attitude against our Tel Aviv ambassador ... and the way this attitude was reflected," the Turkish foreign ministry said in a statement.
"We call on the Israeli foreign ministry, whose behaviour and attitude towards our Tel Aviv Ambassador did not comply with diplomacy, to obey courtesy rules."
In response, Binyamin Netanyahu, the Israeli prime minister, said: "The foreign ministry's protest to the Turkish ambassador was just in its essence but should have been conveyed in an acceptable diplomatic manner."
Ayalon said: "In the future, I will clarify my position in diplomatically acceptable ways."
But an unnamed Turkish foreign ministry official told Turkey's Anatolia news agency that the Israeli statements were "inadequate".
The series that sparked the latest row between the two countries was a Turkish television drama, called The Valley of the Wolves, which Israel says depicts Israeli security forces as kidnapping children and shooting old men.
That followed a drama aired on Turkish state television last October that appeared to portray Israeli soldiers shooting a Palestinian baby at close range.
Ayalon had summoned Celikkol on Monday to express Israel's displeasure over The Valley of the Wolves.
|Lieberman said Israel had no desire to fall out with Turkey
At the beginning of the conversation with the Turkish envoy, the deputy foreign minister told cameramen in Hebrew: "Pay attention that he is sitting in a lower chair ... that there is only an Israeli flag on the table and that we are not smiling."
In a subsequent interview to Israel's Army Radio, Ayalon said: "In terms of the diplomatic tactics available, this was the minimum that was warranted given the repeated provocations by political and other players in Turkey."
An official Netanyahu's office said he had known that Celikkol was being summoned, but that he had been unaware of the manner in which the meeting would be held.
Speaking during a visit to Cyprus on Wednesday, Avigdor Lieberman, Israel's foreign minister, said his country had no desire to fall out with Turkey but urged Ankara to show reciprocal "respect".
"You know regarding Turkey maybe it's time to clarify our position - we are not interested in confronting or arguing with Turkey," Lieberman said.
"We have had good relations with Turkey for many years and we respect the Turkish state and people.
"But that is exactly what we expect in return from them - to treat us with dignity and respect," he said.
The minister urged "direct dialogue even if we don't see eye to eye on some issues".
"I think this is the best way and I hope we can come back to the normal relations between the two countries," he said.