Jose Antonio Alonso said those arrested overnight were involved "in recruiting individuals for jihad" and according to the police had contacts with the "inner core of al-Qaida in Iraq," he said, holding out the possibility of more arrests.
The group consisted of an inner circle which took decisions and two cells, one to recruit new sympathisers, the second devoted to forging documents. It used the internet to establish links with other cells abroad, Alonso said.
Searches of homes and businesses overnight and through the early hours of Monday morning had found "elements that drew police attention".
Substances found such as citric acid and chemical solvents could be "used to make explosive devices" even if some elements essential to bomb-making were missing, he said.
Alonso said the Spanish police had not discovered any plan for an attack on Spanish soil.
"[The 16 men were involved] in recruiting individuals for jihad"
Jose Antonio Alonso,
Spanish Interior Minister
Through overnight and early-morning raids six suspects were detained in the southern city of Malaga, three each in Lerida in the northeast and Nerja in the south, two in Seville in the south and one in the Balearic islands.
A further suspect, said to be Algerian, was detained during the evening in the southern city of Granada.
About 100 officers were involved in the operation.
The interior ministry said eight of those detained were Moroccans, while the rest were made up of a Belarussian, an Egyptian, a Frenchman, a Ghanaian, an Iraqi, a Saudi and a Spaniard.
"The real leader of the network" is a man called Hiyag, alias Abu Sufian, a 25-year-old Iraqi with contacts abroad and in Iraq, where he had "close access to (Al-Qaida leader) Abu Musab al-Zarqawi," the ministry said.
Two of those arrested were working as imams in mosques, one in the Spanish enclave of Ceuta on the Moroccan coast, the other in the southern city of Malaga.
In the latter case, the imam is a 36-year-old originally from Ghana who police believe was involved in trafficking illegal immigrants from Africa.
In the case of the man from Belarus, Andrey M, police said he was variously known as Amin Al Ansari or Sergei Malyshev.
Seven people suspected of financing an Algerian extremist group were arrested on the southern Spanish coast on 9 December.
Spanish police also say they seized
' bomb making' materials
Four of them were released without any charges the following week while three others were remanded in custody for suspected cooperation with a terrorist organisation.
The Spanish newspaper El Pais on Monday published the findings of an investigation that said Spain had a total of 600 Islamist worship centres, or more than twice as many as the 272 Muslim bodies registered with the justice ministry.
"Most of them are in apartments and places beyond the control of the administration," the paper said.