The men were arrested under suspicion of terror offences
The arrests of three men over terror offences are linked to an investigation into threats to kill Prime Minister Gordon Brown, the BBC has learned.
The threats, also against former prime minister Tony Blair, were made in January on a recognised jihadi website.
The group posting the statement called itself "Al Qaeda in Britain" and demanded the withdrawal of British forces from Iraq and Afghanistan.
The men were arrested at Manchester Airport and in Accrington, Lancashire.
They were held in connection with the website threats, which included a demand for the release of Muslim prisoners from Belmarsh high-security prison in London.
Two of the men were about to board a flight to Finland. Counter-terrorist officers from Greater Manchester and Lancashire are now in Scandinavia continuing their investigations.
The arrests were a joint operation between Lancashire Police and Greater Manchester Counter Terrorism Unit.
Detectives have searched the homes of the men, aged 21, 22 and 23.
Two of the addresses searched were on Percival Street, Whalley Range, and Cromwell Street, Audley Range, in Blackburn.
Police have until Thursday to charge the men, release them or seek an extension to their custody.