He held four people hostage during the incident, but they were later released unharmed.
In a statement issued on Wednesday, Counter Terrorism Policing North West said: “Officers from Counter Terrorism Policing North West are continuing with their investigation following the events in Texas. They are working closely with and are supporting US law enforcement.
“As part of the local investigation, two men have been arrested this morning in Manchester. They remain in custody for questioning.
“We continue to work closely with colleagues from other forces.”
Two men arrested in Birmingham and Manchester on January 20 as part of the same probe have been released from custody with no further action.
FBI director Christopher Wray called the stand-off an antisemitic incident, while US President Joe Biden said it was an “act of terror”.
In a press conference held in Texas last Friday, the FBI said Akram was not known and had no prior contact with US intelligence services.
The bureau said it is conducting “rigorous” analysis of Akram’s associates, his online presence and his devices.
Akram had flown to New York on December 29 before he later travelled to Texas and entered the Congregation Beth Israel Synagogue.
Akram – understood to have a criminal record – was investigated by MI5 in 2020 but deemed not to be a credible threat to national security at the time, official sources previously confirmed to the PA news agency.
It is not yet clear how he was able to travel to the US despite his UK criminal record.
The FBI said it is “working hard” to learn more about how Akram acquired the firearm he possessed.
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