That was met with opposition from the Labour Party of Wouter Bos, the deputy prime minister.
"A plan was agreed to when our soldiers went to Afghanistan. Our partners in the government didn't want to stick to that plan, and on the basis of their refusal we have decided to resign from this government," Bos said.
The Dutch mission, based Afghanistan's Uruzgan province, began in August 2006 and involves 1,906 troops.
Since then, 21 Dutch soldiers have been killed there.
The political collapse all but guarantees the Dutch troops will be withdrawn at the end of their mandate in August.
Janan Mosazai, a political analyst in Kabul, said a Dutch pullout would "certainly mean a setback for the so-called international coalition" and its plans of establishing a secure Afghan state.
"And in the short term it would be a tactical setback because Uruzgan is a major transit route for the Taliban insurgency and it would mean a reallocation at least of troops to Uruzgan province," he told Al Jazeera.
The Dutch troops share their base in Tarin Kowt, in Uruzgan province, with Australia's contingent of troops, but Australia is far from keen to take over command of the area.
James Appathurai, the Nato spokesperson in Brussels, said that the Dutch decision would not harm the military alliance's operations in Afghanistan.
"Its obviously a complication, but it is nothing that we couldn't foresee coming," he told Al Jazeera.
"We have 44 countries in this coaltion ... no matter what happens we will manage, we have plenty of countries, plenty of forces."
James Bays, Al Jazeera's correspondent reporting from Afghanistan, said that if the Dutch troops were to pull out it could prompt other nations to consider leaving.
"The real worry in Nato circles - if the Dutch were to pull out - would be that it might start a domino effect. No Nato country in the last eight years has pulled out from Afghanistan completely yet," he said.
"If that was to happen, it might give cover for other countries to say 'we've done our bit ... it's time for someone else to take the burden'."
Nato asked the Netherlands to "investigate the possibilities and desirability of a longer stay in Afghanistan", but extending the Dutch mission would have required unanimous cabinet approval.
The Dutch coalition government, which took office three years ago, had been an uncomfortable alliance from the start and the Nato request tipped Balkenende and Bos into open discord in a parliamentary debate on Thursday.
Opinion polls suggest the Afghan war is unpopular in the Netherlands.
Klaas den Tek, a political correspondent with Radio Netherlands Worldwide, told Al Jazeera a new government was unlikely to endorse a new Afghan mission.
"There is now a majority in parliament which is against the mission in Afghanistan ... after an election I can hardly think there is going to be a new majority that is going to accept a new mission," he said.
Early elections could also threaten Dutch attempts to cope with the global financial crisis.
If an election is held before the unveiling of next year's budget in September, it would effectively nullify an existing agreement to hold off any austerity steps until 2011.
"Elections are likely to be held before the summer, by June at the latest," Vincent van Steen, the home affairs ministry spokesman, told the AFP news agency.
He said Queen Beatrix, the head of state, would consult her advisers on how to proceed.