Zeki Celer, who is the TRNC Labour minister drew criticism after he and his cousins travelled to Aman from Paphos on Wednesday.
Celer had posted a photo from Paphos airport on social media prompting reaction in north Cyprus, reports said.
If I wanted to hide it I would not post a photo of the trip on social media and I would have travelled secretly, he was quoted as saying.
Celer said he has raised the matter of the high ticket prices and an effort was underway to tackle the problem.
Turkish media outlets also reported the matter, saying it was the first time a minister used south Cyprus passport and its airports to go on holiday abroad.
Edited from Cyprus Mail