Belgium's chief prosecutor named Wednesday two brothers, affiliated with the Islamic State group, as the suicide bombers who killed at least 31 people in a recent attack in Brussels, adding that key suspect, who was believed to have been detained, was still on the run.

Belgian media which had reported the arrest of a prime suspect in Tuesday's bomb attacks in Brussels said the person detained was not, in fact, Najim Laachraoui.

25-year-old Laachraoui is also known under his alias, Soufiane Kayal, is believed to be the man seen on CCTV pushing a baggage trolley alongside the bombers and then running out of the Brussels airport terminal. Although other media reports named Laachraoui as the second suicide bomber at the airport.

The Belgian federal prosecutor told a news conference that Ibrahim El Bakraoui, 29, one of two men who blew themselves up at Brussels airport on Tuesday, had left a will on a computer dumped in a rubbish bin near the militants' hideout.

RELATED: Brussels Attack

In it, he described himself as "always on the run, not knowing what to do anymore, being hunted everywhere, not being safe any longer and that if he hangs around, he risks ending up next to the person in a cell" - a reference to suspected Paris bomber Salah Abdeslam, who was arrested last week.

His brother Khalid El Bakraoui, 27, detonated a bomb an hour later on a crowded rush-hour metro train near the European Commission headquarters, prosecutor Frederic Van Leeuw said.

Both men, born in Belgium, had criminal records for armed robbery but investigators had not linked them to Islamist militants until Abdeslam's arrest.

The arrest of Abdeslam seems to have prompted the bombers to rush into an attack in Belgium after months of lying low, according to the testament found on the laptop.

Some Belgian media reports said a forensic link had been established between one of the Brussels bombers, who may have been killed, and the Nov. 13 attacks in the French capital.