Police stopped short of calling Saturday afternoon's blasts, which killed the suspected bomber and wounded two people, a suicide attack. A car blew up in a busy shopping area, followed minutes later by a second explosion nearby.
Shortly before the blasts, Swedish news agency TT received a threatening letter referring to Sweden's presence in Afghanistan and caricatures of the Prophet Mohammad drawn by a Swedish cartoonist. The letter included digital sound files with a recording in broken Swedish and in Arabic.
The incident follows several nervous months in Europe after a U.S. travel alert about possible attacks by militants and a failed bid by a Yemen-based al Qaeda group to use air cargo to send parcel bombs via Europe to America.
German authorities last month said they were on guard against threats of armed attack on civilians of the kind that killed 166 in the Indian city of Mumbai in 2008, but Germany said on Sunday it saw no link with the Swedish attack.
TT said the letter promised attacks over Sweden's presence in Afghanistan, where it has 500 troops with the U.S.-led NATO force, and the cartoons drawn three years ago by Lars Vilks.
"This is a very serious incident, which is being investigated as an act of terrorism," Anders Thornberg, director of operations at the Security Police, said in a statement.
"As far as we know, it looks like he was working for himself, but we have to be really sure so we are investigating whether there could be more perpetrators," he told Reuters.
The police declined to go into further details about the dead man's motives or identity.
U.S.-based SITE intelligence group, which monitors Islamist websites, said a member of Shumukh al-Islam posted a message on Sunday identifying the alleged bomber as Taymour Abdulwahab and cited media reports naming him as Taymour Abdulwahab Al-Abdaly.
A post on a Muslim dating website showed Abdaly was married with two young daughters and looking for a second wife.
In the post he wrote that he was born in Baghdad and moved to Sweden in 1992 and that he studied at the University of Bedfordshire in Luton, which has a large Muslim community.
U.S. terrorism expert Evan Kohlmann told Reuters the suspect had been identified on online forums normally used by militant groups, including al Qaeda, as "holy warrior" Taimur Abdelwahab.
A Facebook page entitled "RIP (rest in peace) Taimour Abdulwahab our brother and friend" has also been set up.
Swedish broadcaster SVT, citing unidentified sources, said the dead man was thought to be a 29-year-old from the small town of Tranas, about 200 km (124 miles) southwest of Stockholm.
Newspaper Expressen said it had found the man's entry on Facebook and that it had a profile picture of two men waving a black flag with Arabic writing on it and Islamic martyr videos.
Police would not comment on a report in daily Aftonbladet on Saturday which quoted a source as saying the man was carrying six pipebombs, of which one exploded, and a rucksack full of nails and suspected explosive material.
"Sweden is panicking of course because this has never been the case before that you have an act of terrorism directed toward the public, and this will of course create fear in Sweden," Vilks told Reuters in an interview.
Sweden did not raise its security threat level -- currently at "elevated," two notches below the top level -- but police stepped up their presence in Stockholm.
Britain, which has suffered similar attacks, said it was in touch with Sweden.
Kohlmann said he suspected the attack was by "a home-grown local extremist who may or may not have connections to any actual terrorist organization."
Prime Minister Fredrik Reinfeldt urged Swedes to remain calm and not let their belief in tolerance and openness be shaken.
Police arrested a man seen getting out of a car brandishing an axe near Reinfeldt's office just before the premier spoke.
The Islamic Association in Sweden condemned the blasts. "The attack is a shock to us all, and strikes at our joint peace and security," Chairman Omar Mustafa said in statement.
The incident began when a car burst into flames near a busy shopping street in the city center, followed by explosions inside the car which police said were caused by gas canisters.
The second explosion, about 300 meters (yards) away and 10-15 minutes later, killed one man and wounded two people.
"Our actions will speak for themselves, as long as you do not end your war against Islam and humiliation of the prophet and your stupid support for the pig Vilks," TT news agency quoted a man as saying in one recording.
(Additional reporting by William Maclean, Ilze Filks and Niklas Pollard; writing by Adam Cox and Patrick Lannin; editing by Elizabeth Fullerton)