Former interior minister Dinos Michaelides and his son, wanted by Greek authorities in connection with money laundering, were arrested on Monday and later released pending extradition hearings later this month.
They were arrested at the Limassol district court, which had ordered their arrest earlier on Monday.
Greece had issued arrest warrants for the pair in connection with a case involving former Greek defence minister Akis Tsohatzopoulos.
The former minister and his son Michalis, who appeared in court with a group of lawyers, did not consent to their surrender to Greece.
The court will hear their cases on July 18.
They were released on a €200,000 bail each and had to surrender their travel documents.
They also have to report to the Yermasoyia police station three times a week.
However, extraditing them to Greece will be difficult as the alleged offences had taken place in the 1990s and Cyprus’ constitution currently prohibits the extradition of Cypriot nationals for events or actions that happened before the country joined the European Union on May 1, 2004.
The investigation concerns alleged kickbacks paid in the purchase by Greece of the Russian TOR-M1 surface-to-air missile system.
The alleged offences took place between 1997 and 2001.