The arrests were carried out in the eastern cities of Valencia and Alicante and in Spain's North African enclave of Ceuta, the police said in a statement.
"Four of those arrested are Spanish nationals of Syrian, Jordanian and Moroccan origin," it said.
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A Syrian and a Moroccan were also taken into custody, it said.
A police spokesperson later announced a seventh arrest, but did not give the individual's nationality or other details.
The operation was still ongoing.
62% of Pakistanis 'don't know' how they feel about Islamic State
The arrests were made in the context of an investigation launched in 2014 into "foreign structures" of Islamic State – which is also called ISIL, ISIS or Daesh – and the Al-Nusra Front, an al Qaeda affiliate in Syria, police said.
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