"One of the suspects is a very important operative in al Qaeda's international structure," Interior Minister Jorge Fernandez Diaz told a news conference.
"This is one of the biggest investigations which has been carried out up until now against the al Qaeda terrorist group at an international level," he added.
Police found the explosives in a flat in the southern town of La Linea de Concepcion in Andalucia, where one of the men was detained on Wednesday, the minister added.
The two others were arrested earlier Wednesday in the central province of Ciudad Real while travelling by bus from the southwestern port of Cadiz to Irun, up near the French border.
"There is a clear indication that those arrested could have been planning an attack in Spain or (elsewhere) in Europe," he told reporters.
One of the two men detained in Ciudad Real had "used uncommon strength to resist arrest, using the military training he received, and special forces had to intervene," he added.
"These are extremely dangerous people."
Police had had the men under surveillance and decided to swoop in and arrest them when it appeared that they were going to leave Spain, he added.
The Turkish man arrested at the flat at La Linea works was a logistics expert for al Qaeda, Diaz said.
The suspect detained in the flat at La Linea was a Turkish national while the other two were from former Soviet republics, which the minister did not name.
Earlier on Thursday Cadena Ser radio, citing police sources, said the suspects were two Chechens and a Turk. It also said that as well as the explosives they had had been in possession of poison.
While Diaz said police had so far found no poison, he added that the secret services of other nations had informed Spain that one of the suspects "has extensive experience in the manufacture of poison and car bombs."
He would not comment on Spanish media reports that the the three men had links to the Pakistan-based Lashkar-e-Taiba militant group blamed for the November 2008 attack on Mumbai that killed 166 people.
The investigation into the three suspects has been assigned to a judge at Spain's top criminal court, the National Audience, which has jusridiction over terrorism cases and international crimes.
Several Islamic extremists have been arrested in recent years in Spain, particularly in Catalonia, in the northeast.
In March, police arrested a suspected member of al Qaeda in the eastern city of Valencia on terrorism charges. They said he ran one of the world's most important jihadist forums dedicated to recruitment and indoctrination.
The Saudi national was known within the organisation as "al Qaeda's librarian," Diaz told reporters at the time.
On March 11, 2004, bombs exploded on packed commuter trains in Madrid, killing 191 people and wounding 1,841 others in a strike by a local cell of Islamic extremists carried out in the name of al Qaeda.
Twenty-one people, mostly Moroccans, were convicted of involvement in those attacks.
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