Turkish players waited several hours in lengthy passport control lines on Sunday night and faced intensive security checks, according to reports from the players published by Turkish media.
Presidential spokesman Ibrahim Kalin took to Twitter to show his anger, slamming the “disrespect” against the national team as “unacceptable”.
“Our state and our people stand by the national team, which will give the best response on the field,” he said.
The team are in the country for a Euro 2020 qualifying fixture, which they will play on Tuesday night. Players and coaching staff were also underwhelmed by their welcome.
The foreign ministry issued a diplomatic protest note to Iceland via the Norwegian embassy, the private NTV broadcaster reported.
There was no immediate explanation for the delay at passport control.
“We have been waiting for three hours. They took everyone’s bags,” Turkey midfielder Emre Belozoglu tweeted from the airport at the height of the altercation.
“What they have done is disrespectful.”
While speaking to media on his way out, TRT World reports Turkish captain Emre Belozoglu met a man who held a toilet brush as a makeshift microphone.
Belozoglu told local media, “We were searched more than once which was unnecessary, and we were told to wait until now.”