Al-Abdaly, 29, was linked to Al-Qaeda in Iraq. In his last will and testament disseminated shortly before he allegedly detonated his explosives on Saturday, he said: "The Islamic State of Iraq has kept its promise," referring to the Al-Qaeda affiliated group.
Al-Abdaly was the only victim of Saturday's attack, during which he allegedly first set a white Audi car alight and then detonated explosives in his backpack, 200 metres away from the car.
If confirmed as a suicide bombing, the attack would be the first of its kind in Sweden.
A few minutes before the explosion, an audio message in Swedish and Arabic was delivered to a news agency and to police, demanding Sweden withdraw its 500 troops from Afghanistan. The message also deplored the 2007 publication in a local Swedish newspaper of a satirical cartoon of the Prophet Mohammed by Swedish artist Lars Villks.
The Islamic State of Iraq in 2007 first vowed to carry out terrrorist attacks in Europe after the publication of Vilks' cartoon.
Vilks has been forced to live under police protection receiving several death threats, including a statement by the Islamic State of Iraq which has offered up to 150,000 dollars for his assassination.
The group has claimed a string of deadly attacks in Iraq, including one in June on the Central Bank of Iraq in Baghdad's highly fortified Green Zone which killed 18 people and injured 55 others.
British police were on Monday searching a house in Luton, north of London in connection with Saturday's attack. Al-Abdaly studied in the UK, at the University of Bedfordshire in Luton.