Dutch authorities said Tuesday they were "seriously" investigating a possible terrorist motive for the Utrecht tram attack because of evidence including a letter found in the gunman's getaway car.

Police were questioning Turkish-born main suspect Gokmen Tanis, 37, and two other men over Monday's rampage in which three people were killed and seven injured, three seriously.

Dutch Prime Minister Mark Rutte had earlier said they "cannot exclude" other motives including a family dispute, but police and prosecutors said on Tuesday that the probe was leaning towards terrorism.

"So far, a terrorist motive is seriously being taken into account. This is based on a letter found in the getaway car among other things and the nature of the facts," police and prosecutors said in a joint statement.

"Our investigation has established no link between the main suspect and the victims."