The UK's counter terrorism police have detained two teenagers in connection with the hostage-taking incident by a British national in a Texas synagogue over the weekend..

"Two teenagers were detained in South Manchester this evening. They remain in custody for questioning," the Greater Manchester Police said in a statement.

A gunman who took four people hostage at a Dallas-area synagogue and died himself as federal agents stormed the temple has been identified as a British citizen.

The day long siege at the Congregation Beth Israel synagogue in Colleyville, about 26km northeast of Fort Worth, Texas, ended in gunfire on Saturday night with all four hostages released unharmed and with the suspect dead.

It was not clear whether the gunman took his own life or was killed by members of the FBI hostage rescue team.

During 10 hours of tense hostage negotiations conducted by authorities on either side of the Atlantic with help from the gunman's family, the suspect was reported to have demanded the release of a Pakistani-born scientist serving a federal prison sentence in the Dallas-Forth Worth area.

Yesterday, the FBI identified the suspect as Malik Faisal Akram, 44, a citizen of the UK but did not say how or when he entered the United States.

One hostage was released unharmed after six hours and the remaining three were freed later

Malik Faisal Akram's brother Gulbar posted on Facebook that the suspect, from the industrial town of Blackburn in the north of England, suffered from mental illness and said relatives had spent all night at a Blackburn police station "liaising with Faisal, the negotiators, FBI etc".

"There was nothing we could have said to him or done that would have convinced him to surrender," Gulbar Akram wrote on the Blackburn Muslim Community's Facebook page.

He said the FBI was due to fly into the UK "later today," saying that the family as a result could say little more.

"We would like to say that we as a family do not condone any of his actions and would like to sincerely apologise wholeheartedly to all the victims involved in the unfortunate incident," Gulbar Akram wrote.

Late yesterday, Greater Manchester Police issued a statement saying officers from Counter Terror Policing North West "have made two arrests in relation to the incident" in Texas, adding that the two teenagers detained "remain in custody for questioning."

US President Joe Biden has called the hostage-taking "an act of terror."

"Allegedly - I don't have all the facts, nor does the attorney general - but allegedly the assertion was he got the weapons on the street," Mr Biden said.

"He purchased them when he landed and it turns out there apparently were no bombs that we know of.... Apparently he spent the first night in a homeless shelter."

Joe Biden spoke about the hostage incident as he arrived in Pennsylvania with the First Lady yesterday

Saturday's siege began in late morning, disrupting Sabbath services as the suspect took the rabbi and three other people hostage.

One hostage was released unharmed after six hours and the remaining three were freed later either shortly before or during the raid by the FBI's hostage rescue team.

SWAT teams from the Colleyville Police Department initially responded to the scene, and FBI agents arriving afterward opened contact with the suspect, who said he wanted to speak to a woman held in a federal prison.

The man, who had seemed to be carrying on a one-sided phone conversation during a Facebook livestream of the service, could be heard talking about religion and his sister, repeatedly saying he did not want to see anyone hurt, the Fort Worth Star-Telegram reported.

The hostage-taker claimed to be the brother of Pakistani neuroscientist Aafia Siddiqui, who is serving an 86-year federal prison sentence on a 2010 conviction for shooting at soldiers and FBI agents, and demanded that she be freed, a US official told ABC News.

Siddiqui is being held at a federal medical lockup in the Fort Worth area. A lawyer representing Siddiqui, Marwa Elbially, told CNN in a statement that the man was not Siddiqui's brother and Siddiqui's family condemned his "heinous" actions.

Colleyville Police Chief Michael Miller told reporters late on Saturday that investigators had no immediate information "that indicates this is part of any ongoing threat."

"We do believe from our engagement with this suspect that he was singularly focused on one issue, and it was not specifically related to the Jewish community," Mr Miller added.

FBI Dallas Special Agent in Charge Matthew DeSarno spoke to the press after the hostages were freed

Although the Texas hostage situation appeared to be an isolated incident, synagogues in New York and elsewhere around the country stepped up security in response and officials condemned anti-semitic acts.

"What happened yesterday at Congregation Beth Israel is a reminder that we must speak up and combat antisemitism and hate wherever it exists," US Vice President Kamala Harris said in a statement.

"Everyone has a right to pray, work, study, and spend time with loved ones not as the other - but as us."

In his Facebook post, Malik Faisal Akram's brother, who also mentioned the death of a younger sibling "barely three months ago," said the family's priority is to have his body returned to the UK "for his funeral prayers although we have been warned it could take weeks."