Police carry out anti-Eta raids in the northeastern province of Navarra.
Officers arrested 13 people, including an imam, in the northeastern Catalonia region, two near Madrid and one at Malaga in the southern region of Andalusia, the interior ministry said.
No weapons or explosives were found, the media reported.
Bruno Cardenosa, a Spanish journalist specialised in international terrorism, said the arrests did not indicate a major threat to Spain from Islamic-led fighters.
He said: “We have seen several operations against Islamic terrorism in Spain in recent years, in which the charges have not been that serious.
“Very probably, most of these suspects will be out in the coming hours or days.”
Spanish police have arrested over 100 suspected ‘terrorists’ since the deadly train bombings in Madrid in 2004.
Police have also stepped up security in the country’s north African enclaves of Ceuta and Melilla – which have a sizeable Muslim population.
Spain is officially home to around 570,000 Moroccans – the largest immigrant group in the country – a majority of whom live in Catalonia.
The arrests came as the Madrid trial of 29 suspects, mainly Moroccans, accused of killing 191 people in the train bombings, comes to a close.
The attack has been linked to al-Qaeda.