But he said the body had not yet been formally identified by DNA or a close family member.
Abdaly, 28, is believed to have died as he tried to set off a car bomb in a busy street. Two people were injured.
Mr Lindstrand told a press conference in Stockholm that after interviewing witnesses, investigators now had "a slightly better picture of what happened".
When asked whether Abdaly had been correctly identified as the bomber in the media, he replied: "Yes".
"We have identified the man who blew himself up, to 98%," he said.
Media reports have said Abdaly was born in Iraq but this was not confirmed at the press conference.
Mr Lindstrand said the bomber had been carrying a bomb belt and had probably intended to cause an explosion in the crowd at the main railway station or a city centre department store.
"If it had all exploded at the same time it could have caused very serious damage," he said.
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The second blast occurred 10 to 15 minutes later on a street about 300m (985ft) away.
'Distorted view' On Monday, British police began searching a house in Luton, in Bedfordshire, north of London, which is believed to have belonged to Abdaly.
It has emerged that Abdaly worshipped at the Luton Islamic Centre Mosque but left after other members accused him of having a "distorted view" of Islam.
A Swedish news agency has released an audio recording apparently made by Abdaly, in which he says oppression against Muslims in Europe will not be tolerated.
He refers to drawings of the prophet Muhammad and to the presence of foreign soldiers - including Swedes - in Afghanistan.
If confirmed as a suicide bombing, the attack would be the first of its kind in Sweden.
Continue reading the main story
- In pictures: Stockholm blasts
Sweden's Prime Minister Fredrik Reinfeldt said at the weekend that the attacks were unacceptable in Sweden's "open society", which he said was a democracy that respected different cultures.
Abdaly was not previously known to the Swedish authorities.The BBC's Security Correspondent Nick Childs says investigators will be trying to determine what links he may have had with the UK.
The blast appears to have been of the same relatively unsophisticated nature as recent attempted attacks in New York, Glasgow and London, says our correspondent.
Such attacks, carried out by individuals, are especially hard for the security agencies to trace and but are an increasing cause for concern, he adds.
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