The 10 are suspected of providing forged passports to organisations linked to Al-Qaeda, including the Pakistan-based Lashkar-e-Taiba, accused of plotting the attacks in Mumbai that killed at least 166 people in November 2008, as well as to the Tamil Tigers.
Police seized forged passports, immigration documents, faked rubber stamps, computers, mobile phones, passport photos, British driving licences and sophisticated counterfeiting equipment in the swoop named Operation Kampai.
Spanish police experts "have travelled to Thailand and are working with Thailand's Department of Special Investigations to analyse the numerous documents seized from the cell," the interior ministry said Friday.
"An initial examination of photographs seized has turned up evidence of the membership of some members of the terrorist organisation the Liberation Tigers of Tamil Eelam."
The LTTE "has perpetrated bloody attacks, many of them by suicides, such as that which killed the former Indian prime minister Rajiv Gandhi in 1991.
"Many of its members were based in Western countries, where they obtained financial assistance for the organisation through extortion and drug trafficking," it said.
The LTTE fought a violent 37-year campaign for an independent Tamil homeland in northern and eastern Sri Lanka before being crushed by government forces last year.
Thai police said on Thursday that the three arrested in Thailand -- two Pakistani men and a Thai woman -- were part of criminal networks tied to "many terrorist attacks".
These included the 2004 Madrid bombings, when blasts on packed commuter trains in a city suburb killed 191 people and wounded 1,841 others. However, Spanish authorities have not confirmed any such link to those arrested.Spanish police detained seven suspects -- six Pakistanis and a Nigerian -- in the northeastern city of Barcelona during the operation.