Police said last night that they had arrested a 40-year-old man suspected of involvement in the shooting.
'Until now, we are looking seriously at a terrorist motive, ' the department said in a statement.
In a statement Tuesday, prosecutors say the nature of the attack and a note found in a getaway auto give them reasons to consider terrorism as a motive.
Prosecutors confirmed that three people died: a 19-year-old woman from the neighboring town of Vianen, and two men aged 28 and 49 from Utrecht.
Police have not released their names or said what their connection to the shooting might be.
"The awful events of yesterday and the loss of our colleague have hit us hard", CEO Pier Eringa said in a statement.
Three of the wounded - a 20-year-old woman from Utrecht, a 21-year-old woman from Nieuwegein and a 74-year-old man from De Meern - remain in a serious condition, according to messages posted on Utrecht Police's Twitter account.
A sea of flowers at the spot where the shooting took place.
Utrecht is the fourth-largest city in the Netherlands, known for its canals and large student population.
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Officials said Tanis has had a long criminal record in the Netherlands involving a variety of offenses - none terror-related - but gave no details. "His role is under further investigation".
Gokmen Tanis, 37, was arrested after a massive eight-hour manhunt on Monday following the shooting in which three people were killed and five others injured.
ASSOCIATED PRESS Construction workers who witnessed Monday's shooting incident in a tram put flowers at the site in Utrecht, Netherlands, on Tuesday.
In the past, he was acquitted of manslaughter but convicted of illegal possession of a weapon and theft.
In a ceremonial session in parliament, Rutte said that because of the attack in Utrecht, "we feel an even stronger bond with the people of Christchurch".
Local media said Tanis had been charged several times over recent years with offences ranging from attempted manslaughter to petty crime in and around Utrecht.
Apparently ruling out reports that the shooting was due to a family dispute, the statement added: "Our investigation has established no link between the main suspect and the victims".
The soccer club posted a message saying: "With great dismay and astonishment, we received the awful news that our trainer of the teams JO19-1 and MO11-2 died in yesterday's shooting incident in Utrecht".