Detectives are continuing to question four men - including one from Chesterfield - held on suspicion of terrorism offences.
Counter-terrorism police swooped on the Whittington Moor area of the town on Tuesday morning and arrested a 31-year-old man who has been identified as Hazhar Star in the national media.
Also known as Andy, he is reported to be the owner of the Mermaid Traditional Fish Bar on Sheffield Road.
Police remain at the scene of the premises.
Councillor Barry Lewis, leader of Derbyshire County Council, said: "Police have done a remarkable job of protecting the public and preventing what could have been a terrible terrorist attack."
Yesterday, the army bomb disposal team - which has been at the scene for much of the week - carried out a controlled explosion to safely dispose of material found during thorough searches.
Chesterfield MP Toby Perkins described the controlled explosion as a 'further worrying development' and added: "Thanks to the police, security services and army who work so diligently and bravely to keep us protected."
On Tuesday, part of Sheffield Road and nearby King Street North were cordoned off while investigations took place and homes were evacuated.
As well as the arrest in Chesterfield, three men, aged 22, 36 and 31, were detained in the Burngreave and Meersbrook areas of Sheffield on Tuesday morning.
All four arrests were made as part of an investigation by the North East Counter Terrorism Unit.
The suspects were taken to a police station in West Yorkshire and detectives have been given until 4pm on Christmas Day to charge, release or apply for a further extension to custody.
Police have not yet officially confirmed the suspects' identities.
At this stage, there is no official word on what type of attack the suspects may have been planning - or when or where they might have carried it out.
Armed police patrolling streets
The UK's terror threat level remains at 'severe', the second highest level.
Derbyshire police are urging people to continue to be vigilant but go about their business as usual.
As announced at the start of the month, armed police are patrolling the streets of Derbyshire over Christmas and New Year to make people feel safer.
If you see or hear something which could be terrorist related, act on your instincts and call the police in confidence on 0800 789 321.
In an emergency, always dial 999.
Visit act.campaign.gov.uk for more information.