Dutch troops have been stationed in Uruzgan province since 2006
Nato has assured Afghans they can rely on its support despite the uncertain future of Dutch troops there following the collapse of their government.
It came after the two largest parties failed to agree over a Nato request to extend the tour of the almost 2,000-strong Dutch contingent past August.
A Nato spokesman said it would provide support to Afghans whatever happened.
Earlier, the governor of Uruzgan said peace and reconstruction efforts would suffer a setback if the Dutch left.
Asadullah Hamdam told the BBC they were playing a vital role building roads, training the Afghan police and providing security for civilians.
"If they withdraw and leave these projects incomplete, then they will leave a big vacuum," he added.
The uncertainty comes as Nato, US and Afghan forces are engaged in a large military offensive against the Taliban in neighbouring Helmand.
Dutch troops have been stationed in Afghanistan since 2006.
They should have returned home in 2008, but their deployment was extended by two years because no other Nato member state offered replacements.
In October, the Dutch parliament voted that the deployment must definitely end by August 2010, although the government of Christian Democratic Prime Minister Jan Peter Balkenende had yet to endorse that vote.
Earlier this week, the finance minister and leader of the Labour Party, Wouter Bos, demanded an immediate ruling from Mr Balkenende.
When they failed to reach a compromise during marathon talks that continued into the early hours of Saturday, Labour said it was pulling out of the coalition.
Later, Mr Balkenende said there was no common ground and offered his cabinet's resignation to Queen Beatrix by telephone.
By Geraldine Coughlan
BBC News, The Hague
The Defence Ministry says the future of the Dutch mission in Afghanistan depends on the new government.
But a new government may prove difficult to establish.
Opinion polls suggest that a handful of parties may be needed to form a coalition.
They also suggest the right-wing opposition Freedom Party, which has called for an end to the Afghan mission, could be the big winner in the general election.
"Where there is no trust, it is difficult to work together. There is no good path to allow this cabinet to go further," he said.
Nato officials swiftly issued a message of reassurance about its operations in Afghanistan, but refused to comment on the internal politics of a member state.
"We have invested a lot in Afghanistan. We will continue to invest in Afghanistan because it is an investment in our own security," Nato spokesman James Appathurai told the BBC.
"Nato will stay as long as necessary. That is a very clear commitment. The Dutch decision is for the Dutch to take, and we will not interfere with that."
Mr Appathurai said Secretary-General Anders Fogh Rasmussen believed the best way forward would be a new smaller Dutch mission, including a provincial reconstruction team to consolidate successes.
The launch in 2001 of Nato's International Security Assistance Force (Isaf) for Afghanistan was the organisation's first and largest ground operation outside Europe.
Mr Rasmussen said six months ago when he began his job that his priority was the war in Afghanistan.
As of October 2009, Isaf had more than 71,000 personnel from 42 different countries including the US, Canada, European countries, Australia, Jordan and New Zealand.
The US provides the bulk of foreign forces in Afghanistan, and President Barack Obama has announced an extra 30,000 American troops for Afghanistan.
The Pentagon has said the next 18 months could prove crucial for the international mission in Afghanistan, after more than eight years of efforts to stabilise the country.
Afghanistan remains a deadly place for foreign forces.
Suicide attacks on Afghan civilians and roadside bomb strikes on international troops are common, with the Taliban strongly resurgent in many areas of the country.