The two men, suspected of links to jihadist groups, appeared in court for the first time on Tuesday afternoon, five days after they were seized in Greece carrying machetes and uniforms.
The judge ordered the pair to be remanded in custody awaiting trial after a preliminary hearing which lasted almost two hours in the northern town of Alexandroupolis.
One of the men is Swedish citizen Mirsad Bektasevic, a 28-year-old man of Bosnian descent from Kungälv, north of Gothenburg, who has previously been convicted of terrorism-related activities. The other is a 19-year-old Yemeni national with a Swedish residence permit, who has not been named by Swedish media.
The two were arrested on Thursday near the Turkish border, 10 days after arriving in Greece by plane from Sweden. Inside their luggage two machetes, army uniforms and other "combat paraphernalia" were discovered, according to police sources.
Greek media reported that the pair were believed to have been on their way to Syria to join Isis forces. Both men deny the accusations and claim they had bought the machetes in Athens and had not intended to use them for criminal purposes.
"They still claim they are innocent and were just touristing. They feel that they are Europeans and should be able to travel freely, but they are beginning to realize the seriousness of the situtation and are more worried now," defence lawyer Menia Polychroni told Swedish broadcaster SVT on Tuesday.
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Bektasevic was locked up in 2007 on conspiracy to commit a terrorist offence after security services raided his apartment and found large quantities of explosives, a suicide belt, and a video showing a man threatening terror attacks against the US Capitol and the White House.
He was sentenced to 15 years in prison but was released in 2011, after which he sought political asylum in Sweden.