Two of the arrested suspects are Russians of Chechen descent Eldar Magomedov and Mohamed Ankari Adamov. They were jailed Sunday on provisional charges of belonging to a terrorist organization.
The third man, a Turk named Cengiz Yalcin, was also jailed on provisional charges of possession of explosives and a device likely to be used in a terror attack.
Spain's Interior Ministry also released photographs of an underground space uncovered by police at Yalcin's home in the southwestern city of La Linea where investigators discovered around 150 grams (5.3 ounces) of an allegedly explosive substance.
Judge Pablo Ruz of the National Court, who jailed the three suspects, described Yalcin as an engineer who had worked in Gibraltar for years and had been involved in providing paragliding lessons for the Russians.
Ruz also said in a court statement that evidence from the U.S. Justice Department suggested Magomedov was involved in terrorist activity in 2010 in Afghanistan and Waziristan, a lawless tribal territory in Pakistan known as a militant hotspot.
It was not clear Saturday if the three suspects had yet been able to appoint defense attorneys.
The ministry has declined comment on whether investigators believe Magomedov and Adamov were practicing paragliding in the hope of unleashing some form of aerial attack.
While a paragliding device designed for a pilot and a passenger might be able to take off with as much as 80 kilograms (176 pounds) of explosives, a model aircraft's payload would clearly be much smaller.