The turnout on Wednesday was 62%, exceeding all expectations, the state-financed broadcaster said.
In the first government reaction to the defeated referendum, Dutch Prime Minister Jan Peter Balkenende said he was "disappointed" over the massive "no" vote, but vowed to honour the outcome.
The parliament, which must formally vote to ratify or reject the treaty, meets on Thursday to discuss the results.
Nine countries have backed the constitution but it needs unanimous approval to take effect.
Calls for ratification
But Europeans elsewhere were calling for ratification of the constitution in other EU states despite the Dutch rejection.
French voters said 'non' to the
EU constitution on Sunday
"We think the ratification process should be taken to its full conclusion. That's a mark of respect for all the people of the European Union," said Martin Schulz, head of the European Socialists group in the European Parliament.
"The constitution should be ratified in each and every member state and be judged by each and every member state," he added, speaking shortly after exit polls indicated that 63% of Dutch voters rejected the constitution.
The future of the EU charter, designed to prevent decision-making gridlock after the European Union expanded from 15 to 25 members last year, has been thrown into doubt by the referendums in France and the Netherlands, both founder members of the half-century old bloc.
EU leaders are expected to discuss the crisis at a Brussels summit in mid-June, although there have been reports that Britain could decide to suspend plans for its own referendum after the Dutch "no."
"It is now up to the (EU leaders) to come forward with a proposal for tackling the institutional issues which the constitution is intended to resolve," said European Socialist Party leader Poul Nyrup Rasmussen.
"The future of the constitution must be clarified," he added.
"We think the ratification process should be taken to its full conclusion"
French defeat referendum
France on Sunday became the first country to vote 'no,' leaving a major question mark over the future of EU integration.
In a national referendum on Sunday, they voted by 55% to 45% to turn down the constitution.
The "No" win had been predicted, but the huge margin of the victory deepened a sense of crisis across the EU.
The French rejection dealt a rude slap in the face of their governing elite, and a potentially fatal setback to the continent's ambitious plans for deeper political union.