Four men were arrested in early-morning raids in South Yorkshire and Derbyshire on Tuesday.
As part of the operation, the Army’s Bomb Disposal Unit was dispatched to an address in Chesterfield.
The immediate area around the property has been cordoned off and local residents evacuated as officers carry out searches.
Three men, aged 22, 36 and 41, were detained at different addresses in Sheffield, while a 31-year-old was held in Chesterfield.
All four were arrested on suspicion of being concerned in the commission, preparation or instigation of acts of terrorism under Section 41 of the Terrorism Act 2000.
The arrests came as police and MI5 tackle a terror threat that is seen as unprecedented.
In addition to five attacks that took place in London and Manchester, Home Secretary Amber Rudd revealed earlier this month that security agencies have foiled nine plots since the Westminster atrocity in March.
Counter-terror teams are running about 500 live investigations involving 3,000 individuals at any one time, while there is also a wider pool of 20,000 subjects of previous probes.
The suspects held on Tuesday are being questioned at a police station in West Yorkshire.
Police said the arrests were “intelligence-led and pre-planned” as part of an ongoing investigation by the North East Counter Terrorism Unit.
A total of five properties are being searched in connection with the probe - four in Sheffield and one in Chesterfield.
A police statement said: “The Army’s Bomb Disposal Unit is currently attending the address in Chesterfield.
“As a precautionary measure and in the interest of public safety, the immediate area has been cordoned off and local residents evacuated while a thorough search is carried out.
“We recognise that local people may have concerns as a result of this activity. We would ask people to remain alert but not alarmed and we are grateful for the assistance and understanding of people locally.”
Police added that loud bangs heard at the time officers entered the premises were part of the method used to gain access.
People living near an address in the Meersbrook area of Sheffield said they were woken at around 5.30am.
Retired Joan Miller, 63, who lives opposite the run-down house, said she looked out of her window to see many plain-clothed armed officers in the street.
Ms Miller said: “It was a very loud bang. It shook the house. I pulled the curtains and saw lots of armed men in the street, so I kept watching because that was quite extraordinary.”
She said the officers shouted “very abruptly” for people to stay in their homes.
Ms Miller and others in the street said they did not know who lived in the house, which is in a dilapidated state.
She said: “It’s been like that for some time and I’d say it was multiple occupancy and that the residents change frequently. That’s all I know.
“All sorts of different people have been living there. I’m assuming it’s flats.”
Police sought to reassure local residents.
Derbyshire Constabulary Assistant Chief Constable Bill McWilliam said: “We of course understand that police activity of this nature can be unsettling.
“However, please be reassured; the arrest we wanted to make has been made.
“Our advice remains to be vigilant, which is not different to our day-to-day advice in the current climate, but continue to go about your business as usual.”
South Yorkshire Police Superintendent Una Jennings said: “I understand our local communities will have concerns about this morning’s police activity but I want to offer my reassurance that we will continue to serve and protect the public of South Yorkshire.
“We work very closely with our colleagues at the North East Counter Terrorism Unit and we will ensure we maintain these strong links in order to provide a high level of service and delivery to everyone in our community. Public safety is our utmost concern.”