Counter-Terrorism Police have been granted a second extension to question three suspects from Keighley who were arrested on May 1.
The suspects, two men and a woman, were arrested on suspicion of preparation or instigation of acts of terrorism along with a suspect from Angelsey and a teenager from Swindon, who has been released without charge.
Detectives will be able to hold and question the individuals until May 15.
Detective Chief Superintendent Martin Snowden is Head of Counter Terrorism Policing North East. He said: "I appreciate the concern these arrests have caused within our communities and in particular the impact of speculation around them on social media.
"Such speculation can be very damaging, creating widespread and unnecessary fear. Please be reassured that there is not believed to be any immediate risk to the public in connection with our ongoing investigation.
"Public safety remains our utmost priority and we will continue to share more information with our communities as and when we are able. In the meantime, we’d ask people not to be alarmed and to go about their business as normal."