Britain's foreign minister Liz Truss on Sunday condemned a hostage-taking at a synagogue in Texas as an "act or terrorism and anti-Semitism".
And a man identifying himself as the hostage-taker's brother said in a post to Facebook that his brother had suffered from mental health problems.
In a statement posted on Twitter, Foreign Secretary Truss wrote: "My thoughts are with the Jewish community and all those affected by the appalling act in Texas.
"We stand with US in defending the rights and freedoms of our citizens against those who spread hate."
In Manchester, northwest England, Assistant Chief Constable Dominic Scally of the region's counter-terrorism team, confirmed the assailant's identity as Malik Faisal Akram.
Akram was from Blackburn, also in the northwest, said Scally.
"Police forces in the region will continue to liaise with their local communities, including the Jewish community, and will put in place any necessary measures to provide reassurance to them," he added.
'Mental health issues'
On the Facebook page of Blackburn's Muslim community, a man identifying himself as Gulbar, the hostage-taker's brother, said he had been shot dead.
"We would like to say that we as a family do not condone any of his actions and would like to sincerely apologize wholeheartedly to all the victims involved in the unfortunate incident," he added.
Gulbar wrote that during the incident, he had been liaising from England with law enforcement at the scene.
"Although my brother was suffering from mental health issues we were confident that he would not harm the hostages," he wrote.
But he added: "There was nothing we could have said to him or done that would have convinced him to surrender."
His family was devastated and their priority now was to get his brother's body back to Britain for his funeral.
US authorities have launched an investigation with "global reach" into a 44-year-old Akram who was killed after holding four people hostage at the synagogue.
Akram was reportedly calling for the release of a convicted terrorist known as "Lady Al-Qaeda".
The four hostages -- including a respected local rabbi, Charlie Cytron-Walker -- were all released unharmed Saturday night. After the incident, the Jewish community and US President Joe Biden renewed calls to fight anti-Semitism.
Police did not say whether the assault team killed the man or whether he killed himself.
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