Explosive material was seized at an address in San Roque where a Turkish man was arrested. Two other men were held near Almuradiel.
They are thought to have been planning an attack in Spain or elsewhere in Europe, according to the Spanish Interior Minister Jorge Fernandez Diaz.
The arrests are part of one the biggest international operations to date against al-Qaeda, Jorge Fernandez Diaz said.
The material is currently being tested but is thought to be enough to “destroy a bus”, he told reporters.
Jorge Fernandez Diaz also said that one of the suspects was a senior al-Qaeda operative with extensive experience “in the manufacture of poison and car bombs”.
One of the men put up “massive resistance” during the arrests, he added.
Police found the explosives in a flat in the southern town of La Linea de Concepcion in Andalusia and arrested a Turkish national at the address.
The two other suspects were travelling on a bus from Cadiz on Spain’s Atlantic coast to Irun near the French border when they were seized in a lay-by near Almuradiel by a police special operations group, Jorge Fernandez Diaz said.
Both men are from former Soviet republics, but the minister did not say which ones.
Police suspect that at least one suspect has attended training camps in Pakistan, reports say.
Al-Qaeda in the Arabian Peninsula had issued a message at the beginning of July looking for Spanish-speaking “lone wolves” as operatives, according to Spain’s El Pais newspaper.
In March, Spanish police arrested a suspected al-Qaeda member in the eastern city of Valencia on terrorism charges.
They said he ran one of the world’s most important jihadist forums dedicated to online recruitment and propaganda operations.
The man, a Jordanian-born Saudi Arabian citizen, was known within al-Qaeda as “the librarian”, Jorge Fernandez Diaz told reporters at the time.
In March 2004, an al-Qaeda linked bomb attack on three packed commuter trains in Madrid killed 191 people and injured 1,841 others.
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