The suspects were held on Thursday morning in Manchester and Birmingham, Greater Manchester Police (GMP) said.
The men, whose ages have not been released, are "in custody for questioning" and were held as part of an "ongoing investigation", GMP added.
Earlier this week, two teenagers were arrested in Manchester by officers from Counter Terror Policing North West and released without charge on Tuesday (January 11).
The FBI in Dallas have said there was nothing to suggest a wider terror plot.
It is understood this remains the case and the latest arrests are not as a result of concerns over a broader threat to the public.
The hostages were released unharmed while US President Joe Biden branded the incident "an act of terror".
In a webinar hosted by the Anti-Defamation League on Thursday, FBI director Christopher Wray said the incident was "antisemitism", which would not be tolerated.
He said: "This was not some random occurrence. It was intentional. It was symbolic, and we’re not going to tolerate antisemitism in this country."
The FBI continues to search phones and other devices as it investigates why Akram targeted the particular synagogue, he added.
Audio footage appeared to reveal 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."
Akram was investigated by MI5 in 2020 but deemed not to be a credible threat to national security at the time, official sources confirmed to the PA news agency.
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.
Akram was issued with an exclusion order from Blackburn Magistrates' Court in 2001, banning him from going near the building, sources confirmed to PA.
The order came as a result of his behaviour in an incident on the day after the September 11 terror attacks in the US, during which he reportedly shouted abuse at court staff.
Born in 1977, his criminal history is understood to date back to 1995 when he would have been about 18 years old.
After that he spent time in and out of jail, first in 1996 for violent disorder.
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