A car blew up in a busy shopping area on Saturday afternoon, followed moments later by a second explosion nearby.
Witnesses said a man found dead after the second blast had been carrying an explosive device. Two people were hurt.
Police are investigating an email sent shortly before the blasts threatening attacks because Sweden had sent troops to Afghanistan.
Sweden has some 500 soldiers deployed in Afghanistan as part of the international military force.
Previous attacks
The email, which was sent to the country's security service and the TT news agency, called for "mujahideen" - or Islamist fighters - to rise up in Sweden and Europe, promising Swedes would "die like our brothers and sisters".
It also attacked the country for caricatures of the Prophet Mohammed drawn by Swedish artist Lars Vilks.
"The mail was about one man," police spokesman Ulf Goransson told a press conference on Sunday.
"He was not satisfied with developments in Sweden regarding [the fact] that we have military troops in other countries, that there had been protests and that there have been said bad things about the Prophet [Mohammed].
"But we are still analysing this email so it's too early to say anything more."
While the investigation is at an early stage, the nature of the explosions does look similar to previous attempted attacks in New York, Glasgow and London, says the BBC's defence and security correspondent, Nick Childs.
Saturday's blasts struck as people were out Christmas shopping.
The car exploded on the busy shopping street of Drottninggatan at 1700 (1600 GMT) and the second blast occurred 10 to 15 minutes later on a street about 300m (300yds) away, police said.
The car had contained gas canisters and had "exploded with a series of minor explosions", police spokesman Ulf Johansson told the BBC.
A man found dead near the site of the second explosion has not been named.
Unconfirmed reports in Sweden's Aftonbladet newspaper said he had been carrying pipe bombs, as well as a backpack full of nails.
Eyewitnesses saw him lying on the ground with blood coming out of his stomach.
Tweeting about the blasts, Foreign Minister Carl Bildt said a terrorist attack that could have been "truly catastrophic" had failed.
In November, Sweden raised its terror alert level from low to elevated because of a "shift in activities" among Swedish-based groups thought to be plotting attacks.
A security official said the threat level had not been raised as a result of Saturday's attacks.
www.bbc.co.uk/news/world-europe-11978389
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