The three men, aged 28, 33 and 30, arrested by the counter-terrorism officers, are in custody at a police station in central London, the Metropolitan Police said today.
A search linked to these arrests has been carried out in the East Midlands, while searches at two addresses in London are ongoing, police said.
The latest arrests follow dawn raids in London on Thursday in which a 40-year-old man was arrested on suspicion of conspiracy to possess and supply fraudulent documents, the BBC reported.
But a 33-year-old man, who was arrested on the same day on suspicion of being concerned in the commission, preparation or instigation of acts of terrorism, remains in custody.
In his case, a warrant has been granted by the courts to allow the police to detain him until December 11 if necessary.
Police said that searches taking place at five residential addresses - four in south-east London and one in Stoke - in connection with Thursday's arrests are now over.
A 28-year-old man was arrested at the same port on Monday, and under the same operation, two men, aged 24 and 40, were arrested in east London.
All five men remain in custody and warrants for their extended detention have been granted until December 14.
The terror threat level in the UK was raised from substantial to severe in August.
Fears of a terrorist attack in the UK have been heightened in the wake of the rise of Islamic State, the extremist group that has taken over large swathes of Iraq and Syria.
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