A foreign ministry source confirmed a report from Athens News Agency ANA that a visit request by Austrian Interior Minister Johanna Mikl-Leitner had been turned down. "We confirm the report," the source told AFP.
The snub came a day after Greece recalled its ambassador to Vienna for consultations in retaliation to Austria's decision to leave Athens out of a Balkans migration meeting this week.
Austria has repeatedly accused Greece of failing to police its borders properly and allowing an excessively high number of migrants to continue their journey northwards.
At a meeting of EU interior ministers on Thursday, Mikl-Leitner called into question Greece's place in the passport-free Schengen zone.
"If it is really the case that the Greek external border cannot be protected, can it be still a Schengen external border?" she wondered.
An angry Greek migration minister Yiannis Mouzalas later retorted that Mikl-Leitner was "falsifying the truth" and "dragging Austria into increasingly hostile acts towards Greece and the EU."
"Our country guards its borders, which are also Europe's borders, in the best possible way. This is a fact confirmed by (EU border agency) Frontex, the European Commission and other institutions," Mouzalas said in a statement.
The Austrian interior ministry said Mikl-Leitner told her Greek colleagues in Brussels that she could come to Greece "to explain Austria's position in detail directly".
The ministry said it remained available "if Greece prefers to conduct the conversation at a later stage".
Greece believes Austria has encouraged a series of border restrictions by Balkan states along the migrant trail to northern and western Europe that has caused a bottleneck on its soil.
Thousands of refugees have been stranded in Greece after Macedonia denied all passage to Afghans and ramped up document controls for Syrians and Iraqis.
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On Friday, there were some 3,000 people waiting to cross at the border post of Idomeni and another 25 buses full of migrants parked a short distance away, local police said.
Macedonian police had only allowed some 150 people to cross since Thursday, Greek police said.
EU migration commissioner Dimitris Avramopoulos said the European Union's migration system could crumble if the number of migrants did not fall before a crucial meeting of EU leaders with Turkey in Brussels on March 7th.