Police describe the attack, in which two people were killed and three seriously injured, as a terrorist act.
According to the police, the perpetrator had no firearm.
Manchester's police chief Stephen Watson says in a written statement that the death was "a tragic and unforeseen consequence of the urgent measures my police officers took to put an end to this brutal attack".
Another person has received a gunshot wound that is not life-threatening, according to the police.
Arrested earlier this year
The suspected terrorist, a 35-year-old British citizen of Syrian origin, was shot dead by police at the scene.
The man was arrested on suspicion of rape earlier this year. He was released on bail in connection with the attack in Manchester, writes The Guardian.
A police source tells BBC that he was suspected in the rape case but not yet charged.
The suspect was known to the police, but not to anti-terror authorities or in contexts related to terrorism.
Nothing indicated that he would do something like this, says a source to The Guardian.
On Friday, the father of the suspected murderer released a statement on social media stating that the family is in "deep shock" and that they condemn the act.
"We completely dissociate ourselves from this attack and express our deep shock and sorrow over what has happened. Our hearts and thoughts are with the victims and their families, and we pray for their strength and comfort."
"Torn away"
Prime Minister Keir Starmer visited the synagogue on Friday, after promising a few hours earlier to "do everything to keep our Jewish population safe".
At a memorial vigil, Rabbi Daniel Walker described the two victims, two men who were 53 and 66 years old, as two "truly wonderful" people whose lives were "torn away when they tried to pray as Jews on the holiest day of the year, Yom Kippur", writes AFP.
The attack occurred on Thursday during a prayer meeting. The perpetrator first drove into people and then attacked with a knife. The man had a fake bomb belt on him when he was shot dead by the police.
