Two teenagers, who were arrested in Manchester in connection to an attack on a synagogue in Texas, have been released without charge.
But UK officers from the Counter Terrorism Policing North West unit are continuing to lead a local investigation and are supporting officers in the US, Greater Manchester Police said.
Malik Faisal Akram, from Blackburn in Lancashire, was killed after holding four people hostage in a 10-hour stand-off at Congregation Beth Israel synagogue in Colleyville, Texas, on Saturday.
Akram - who had flown from the UK to the US and bought a weapon - was shot dead after the FBI stormed the building.
All four hostages were unharmed.
Greater Manchester Police said on Sunday night two teenagers, whose ages and genders were not confirmed, had been arrested and were being questioned.
They have now been released without charge, the force said on Tuesday evening.
An address in North Manchester has also been searched.
President Joe Biden has branded the Texas attack “an act of terror”.
Temporary Assistant Chief Constable Dominic Scally, who is leading the Counter Terrorism Policing North West unit, said: "CTP North West is continuing to assist with the investigation which is being led by US authorities. Overnight, constructive meetings with colleagues from the United States have taken place.
"As part of our enquiries, we're also working with colleagues in other forces and Lancashire Police are working with communities in the Blackburn area to put measures in place to provide reassurance."
Akram is said to staged the siege to demand the release of Pakistani neuroscientist Aafia Siddiqui, who was convicted of trying to kill US army officers in Afghanistan, and is in prison in Texas.
He had travelled to New York from Manchester on December 29 - just over two weeks before the siege - with a return flight booked for February 2, ITV News understands.
It is also understood that the British man became a subject of interest (SOI) for MI5 when he was investigated in 2020 but was assessed not to pose a credible threat to national security so was downgraded and marked a “closed” SOI.
He was not subject to a live investigation when he travelled to the US, the Press Association news agency understands.
It is not clear how Akram, who had a criminal record in the UK, was able to travel to the US and buy a gun.
According to reports, Akram stayed at a homeless shelter and is believed to have bought a gun on the street.
Akram’s family said they were “absolutely devastated” by what had happened and “do not condone any of his actions”.
The family statement was attributed to Akram’s brother Gulbar on the Blackburn Muslim Community Facebook page.
Gulbar said he had been involved in negotiating from the UK with his sibling during the ordeal and said his brother “was suffering from mental health issues”.