British security services had assessed the gunman in a prior investigation and found he was no longer a threat at the time he travelled to the US.
The United Kingdom's counterterrorism police have said the teenagers were detained in South Manchester and remain in custody for questioning.
US security forces killed the gunman who held four people including a rabbi as hostage in the Congregation Beth Israel synagogue in Colleyville.
Family of Malik Faisal Akram (44) apologises to victims, saying they were helping police negotiate with Akram who had been suffering from "mental health issues".
US President Biden calls Texas synagogue stand-off a terrorist act, and appears to confirm the attacker had sought release of convicted scientist Aafia Siddiqui.
All hostages of Texas synagogue have been freed some ten hours after a man has demanded release of a woman in prison because of terrorism.
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