(Recasts with new arrests)

LONDON, Oct 14 (Reuters) - British police arrested three men and three women on Tuesday in a counter-terrorism operation linked to the civil war in Syria.

Counter terrorism officers detained the suspects in London, Portsmouth, on England's south coast, and in Farnborough, west of the British capital.

The group, aged between 23 and 57, were being held on suspicion of range of terrorism offences.

"Officers would like to reassure residents that the police activity today is in relation to conflicts overseas and is not linked to any immediate threat to local communities or anywhere else in the UK," the South East Counter Terrorism Unit (SECTU) said in a statement.

Britain raised its international threat level to the second-highest classification of "severe" in August, meaning an attack was considered highly likely.

British Prime Minister David Cameron has said Islamic State militants battling for territory in Syria and Iraq pose a grave security risk to Britain.

On Monday, London police arrested three men as part of what they said was an ongoing investigation into "Islamist terrorism".

The men, aged 24, 21 and 25, were arrested in central London

on suspicion of being concerned in the commission, preparation or instigation of acts of terrorism.

Last week, five men were arrested in raids by police, including armed officers, and a European security source familiar said detectives believed they might have foiled a plot to attack targets in Britain which was in the early stages of planning.

Three of the suspects remain in police custody but two were released on Monday. (Reporting by Michael Holden; editing by Guy Faulconbridge)

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