"His position is that he admits to a terrorist crime and accepts therefore that he will be detained", Johan Eriksson Akilov's lawyer said during a court hearing held to decide whether he should be kept in custody.
Legal documents show Akilov had asked for Eriksson to be replaced by a Sunni Muslim lawyer, but the court denied his request.
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British man Chris Bevington, 41, a husband and father, was among the victims.
Security services previously said Akilov had expressed sympathies with extremist organisations, including Islamic State, but had not been viewed as a threat.
He is suspected of driving the truck into pedestrians on Drottninggatan (Queen Street), a busy shopping street in the center of Stockholm, on Friday before crashing it into a department store. The police said last week they had intelligence on Akilov in 2016 that they could not verify. The others have not been publicly identified.
An 11-year-old who died after she was mown down by a stolen truck that ploughed into a crowd in Stockholm has been named. Eight of those injured, two seriously, are still being treated in hospital.
A second man arrested over the attack would face no charges but is set to be deported, police said.
There were no more details on which country Uzbekistan had told.
Friday's attack shocked Sweden, known for its welcoming policy toward migrants and refugees.
Mr Akilov reportedly ran from the scene of the attack, still covered in blood and glass, and was arrested hours later in a northern suburb of Stockholm.
He was one of an estimated 12,000 rejected asylum seekers who remained in the country after being ordered to leave.
Information for this article was contributed by David Keyton of The Associated Press and by Christina Anderson and Milan Schreuer of The New York Times.