In Thursday's attack two men, Adrian Daulby, 53, and Melvin Cravitz, 66, were killed after a UK man of Syrian descent drove a car into pedestrians and then began stabbing people outside Manchester's Heaton Park Hebrew Congregation Synagogue during Yom Kippur, the holiest day in the Jewish calendar.
The attacker, shot dead by officers at the scene, was not carrying a firearm, said Greater Manchester Police chief constable Steve Watson although one of those killed suffered a gunshot wound.
"It follows therefore this injury may have been sustained as a tragic and unforeseen consequence of the urgently required action taken by my officers to bring this vicious attack to an end," Watson said in a statement.
Watson said another worshipper is believed to have suffered a non life-threatening gunshot wound and that it is thought both victims were close together behind the synagogue door, as worshippers tried to prevent the attacker from gaining entry.
The police complaints watchdog said it was carrying out an investigation into what happened.
Police have named the attacker as Jihad al-Shamie, 35, and said they could find no records to show he had been referred to the government's anti-radicalisation program.
The man was on police bail for an alleged rape when he carried out the synagogue attack, sources told the Press Association news agency.
Shamie, wielding a large knife, shouted, "This is what you get for killing our children" as he tried to break the door in, Alan Levy, chairman of the synagogue's trustees, told ITV News.
In a statement on Facebook, Shamie's family said they were in "profound shock" and wanted to distance themselves from what they called his "heinous act".
The government of the United Kingdom vowed to redouble its efforts to tackle anti-Semitism as the Jewish community reeled from the attack.
Prime Minister Keir Starmer visited the site of the attack and spoke with police and ambulance workers, praising "the degree of professionalism and speed" they showed in their response.
When Deputy Prime Minister David Lammy spoke at a vigil outside the synagogue on Friday, he was heckled by people who said "Jews don't want to live here anymore" and urged him to stop the pro-Palestinian marches that have taken place in UK cities regularly since the start of the Gaza Strip war.
Many Jewish leaders noted that they were the only faith in the UK that routinely required security at its institutions.
Last month, Starmer announced that the UK was recognising a Palestinian state in the hope of reviving peace for Palestinians and Israelis, a decision decried by Israel as a "huge reward to terrorism".
Israel has accused the UK of allowing rampant anti-Semitism to spread through its cities and universities and repeated that criticism after Thursday's attack.
UK interior minister Shabana Mahmood criticised pro-Palestinian protests that took place hours after the Manchester attack, calling them un-British and dishonourable and urging people to show a bit more "humanity and some love towards a community that is grieving".
with PA
