Two men were arrested in Manchester on Wednesday (January 26) "as part of the local investigation".
Police were also given more time to question two people held in Birmingham and Manchester on January 20.
Greater Manchester Police said officers from Counter Terrorism Policing North West were continuing their investigation and working closely with US law enforcement.
The siege began at around 11am (4pm GMT) when police were called to the Congregation Beth Israel synagogue in Colleyville, near Dallas.
Akram had entered the place of worship during a morning service by pretending to be homeless, before pulling out a gun.
One hostage was released after six hours, while the other three - including the synagogue's rabbi - escaped several hours later.
Thanks for reading. If you value what we do and are able to support us, a digital subscription is just £1 per month for the first two months. Try us today by clicking HERE.