The coastguard had recovered 31 bodies by last night and a man previously pulled alive from the water died later in hospital.
The aircraft was carrying six crew and 26 passengers when it went down, a coast guard spokesman said.
The vintage aircraft ditched into the shallow Wadden Sea about 37 miles north of Amsterdam yesterday afternoon.
The Dakota was on a pleasure flight for aviation enthusiasts, members of the Dutch Dakota Association that owned and flew the aircraft.
A small flotilla of navy and fishing boats headed for the wreckage of the Dakota from Den Helder soon after the crash.
Television footage showed the aircraft's tail jutting out of the water, with the mangled remains just under the surface.
A spokesman for the Dutch Royal House said Queen Beatrix was "deeply shocked" by the crash and sent her sympathy to the families of victims.
The aircraft's pilot reported engine trouble shortly after taking off from the North Sea island of Texel and was planning an emergency landing at Den Helder's small airport. The Dakota was heading for Schiphol airport, Amsterdam.
Anne Groeneveld, chairperson of the Dutch Dakota Association, said the plane "was in perfect technical condition. It was recently checked by the Dutch Aviation Association.
"It doesn't fly many miles each year and it undergoes regular preventive maintenance. There is absolutely no reason to suspect technical malfunction."
The cause of the crash was not immediately known. Identities of the victims were not immediately released.
The crash came just two months after a C-13 Hercules transport plane crashed in the southern Dutch city of Eindhoven, killing 34 passengers and crew. The US-built Belgian air force plane carrying members of the Dutch army's Fanfare band crashed at the side of the runway in the Welschap military sector of the Eindhoven Airport.
In October 1992, an El Al Jumbo Jet transport plane slammed into a block of flats in Amsterdam, claiming 43 lives.Reuse content