Akram, 44, originally from Blackburn in Lancashire, was shot dead when the FBI entered the building in Texas on January 15 following a 10-hour stand-off.
Announcing the latest development, Greater Manchester Police said: “Officers from Counter-Terror Policing (CTP) North West continue to support US authorities with their investigation into the events in Texas.
“As a result of this ongoing investigation, two men have been arrested this morning in Birmingham and Manchester.
“They remain in custody for questioning.
“CTP North West officers continue to liaise with and support colleagues from other forces.
“Communities defeat terrorism and the help and support we get from the public is a vital part of that.
“So, we would urge everyone to remain vigilant, and if you do see anything suspicious then please report it, in confidence, to police via the anti-terrorist hotline or gov.uk/ACT
“It won’t ruin lives but it may well save them.”
Two teenagers arrested in Manchester following the incident were released without charge on Tuesday.
The hostages were released unharmed while US President Joe Biden branded the incident “an act of terror”.
Audio footage appeared to show a tense final conversation between Akram and his younger brother Gulbar, in which the armed 44-year-old was urged to surrender by his sibling.
The recording, obtained by the Jewish Chronicle from a security source, features Gulbar pleading with his brother to stop.
He said: “Why are you doing that, man? What you doing that for, you know? What’s wrong with you?”
Akram’s replies include his request to die a martyr, as well as some expletive-laden and rambling attempts to justify his actions.
Gulbar, still trying to reason with the hostage-taker, said: “Why have you come to die for? Why though?
“Come on, man.
“You don’t need to do this, whatever you’re doing, man.
“Just pack it in, you’ll get a bit of time and you’ll come out.
“Think about your kids, man, these guys are innocent – these guys you’ve got there are innocent people, man.”
The 44-year-old, originally from Blackburn in Lancashire, was investigated by the security services in 2020 but deemed not to be a credible threat to national security at the time, official sources confirmed.
At one point he demanded the release of Pakistani neuroscientist Aafia Siddiqui, who was convicted of trying to kill US army officers in Afghanistan, and is in prison in Texas.
It is not yet clear how Akram, who had a criminal record in the UK, was able to travel to the US two weeks ago. US officials believe Akram had a visa, arrived at John F Kennedy International Airport in New York and bought the handgun used in the incident.
According to reports, he stayed at a homeless shelter and is believed to have bought a gun on the street before taking four people hostage at the synagogue, one of whom was released after around six hours.
US President Joe Biden branded the incident “an act of terror” and UK police are working with authorities in America on the investigation.