Two men have been arrested under the Terrorism Act in operations in Huddersfield and Sheffield which are not connected to the Manchester terror attack, police said.
Loud bangs heard in the Crosland Moor area of Huddersfield were made by officers gaining entry to a property, police said.
A spokeswoman for the North East Counter Terrorism Unit said: "We understand that people may have concerns as a result of this activity and we are grateful for the patience and understanding of the public while these inquiries are carried out."
The spokeswoman said the men - aged 24 and 29 - are both from Huddersfield and were arrested on suspicion of offences under Section 5 of the Terrorism Act.
They were detained at separate locations in Huddersfield and Sheffield.
She said searches were being carried out in properties in both locations.
The spokeswoman said: "There are no connections to the recent incident and investigation in Manchester.
"The operation is based on recently received intelligence."
Social media reports said loud bangs were heard in the area on Thursday evening.
The spokeswoman said: "The public may have heard loud bangs at the time that police entered the property.
"We would like to reassure you that this was part of the method of entry to gain access to the property."
The raid in Sheffield appears to have been in flats in the Kelham Island area of the city.
Twitter users reported an area cordoned off less than a mile from the city centre with a large amount of police activity, including many armed officers.