Tehran did not confirm how many Slovaks had been detained, but Slovak Foreign Minister Miroslav Lajcak said eight Slovaks were under arrest in Iran.
"They came to Iran as tourists but behaved inappropriately and had unconventional devices in their possession," Iranian foreign ministry spokesman Abbas Araqchi told ISNA news agency.
"They broke the laws of the Islamic Republic of Iran and were arrested by the relevant authorities."
Araqchi did not say when or where they were detained, but added "an investigation has begun and their case will be referred later to the judiciary".
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Slovak Prime Minister Robert Fico said on Saturday that the group detained in Iran "are facing very serious charges" without giving any further details.
"It's a very sensitive case. I can only say that Iranian authorities are talking about very serious charges against our citizens," he added.
On Sunday, his foreign minister said: "I can confirm that eight Slovak citizens have been arrested in Iran".
"The ministry has been taking steps since May 22, when we learned about the arrest," Lajcak said in remarks broadcast on national public television.
"We are in everyday contact with the Iranian foreign ministry. (The) Slovak consul in Tehran has visited the arrested tourists -- they are alive and in good health."
"I don't feel good about the fact that journalists have taken interest in the case. No similar case has ever been solved by newspaper stories," said Lajcak.
"I cannot give you more information because it could harm the prospects of our citizens to be released and safely moved home."
Slovakia's SME newspaper reported the paragliders had been arrested in Iran "more than three weeks ago for taking pictures of military objects from above".
Another Slovak citizen was arrested in the country last year on allegations of spying for the US Central Intelligence Agency and paraded on state television.
State television said he was accused of contacting Iranian scientists to seek information on "the country's scientific progress".