Ismail Abedi had been ordered to attend the public inquiry into the May 2017 terror attack but boarded a flight to Istanbul from Manchester Airport at the end of August and has not returned.
They said they were “shocked” how the 28-year-old was allowed to leave the country a day after he missed a flight when he was stopped and questioned by police and told them he was going on a three-week break.
On Friday, Mr Justice Sweeney sitting at Manchester Civil Justice Centre granted an application from inquiry chair Sir John Saunders to issue a bench warrant against Abedi.
Paul Greaney QC, for the applicant, argued Abedi had “important” evidence to give on his younger brother’s path to extremism.
This week, the inquiry has head how their father, Ramadan Abedi, was associated with the Libyan Islamic Fighting Group, a militia that had links with terror organisation al-Qaeda.
Another Abedi brother, Hashem, 24, was jailed for life last year for the 22 murders by assisting the bomb plot.
Mr Greaney said: “The question that the inquiry would like to pose is was Ramadan Abedi a violent Islamist extremist and if so did that rub off on his sons.”
He said the inquiry also wants to know if Salman and Hashem had received military training in Libya after photographs of the pair holding weapons were found on Ismail’s phone.
Another area to probe would be to ask Ismail if it was “just a coincidence” that Salman spent increased time with mutual friend Abdalraouf Abdallah, 28 – later jailed for terrorism offences – in 2015 and 2016 when he was said to have eschewed his previous partying lifestyle and become more religious, said Mr Greaney.
Finally, Abedi has potential relevant evidence to give, said Mr Greaney, on the preparation of the bomb given his DNA was found on a hammer in a car used to store the explosives.
Rebecca Filletti said he was held in custody for two weeks after the attack in 2017 and he was detained again in August this year when his phone was examined.
Neither investigation resulted in any criminal charges.
She also pointed out her client aired caution over the issue of forensics as the court would be aware DNA is transferable and the hammer was a moveable object.
Last month, lawyers for Abedi issued a statement in which they said he was unwilling to give evidence and the questions asked by the inquiry are “essentially the same as he was asked by the police”.
He added requiring him to attend before the inquiry would place him and his family at risk.
It is understood Abedi’s wife and child flew out separately to join him.
At the time of the bombing, Ramadan Abedi was in his homeland of Libya where he remains and has not co-operated with the inquiry. Police still want to question him as a suspect.
Friday’s hearing was told Ismail Abedi could face criminal prosecution if he does not attend the inquiry before it ends.