* Last government collapsed over troop pullout
* Small opposition parties agree to back mission
* Polls show majority of voters opposed
(Adds new Rutte quote, German vote)
By Aaron Gray-Block
AMSTERDAM, Jan 28 (Reuters) - The Dutch government won parliamentary support on Friday to send a mission to Afghanistan to train police, a year after the last coalition collapsed because of divisions over whether to pull its troops out.
A total of 545 men and women will be deployed, including police and military trainers, soldiers and military command specialists. The mission is to become fully operational in May.
Prime Minister Mark Rutte won over three small opposition parties in the final hours ahead of a vote seen as a key test of his minority Liberal-Christian Democrat coalition.
"It is in our interest to prevent the consequences of extremism in Afghanistan and it is important because we are committed to Afghanistan and cannot just give up on it," Rutte said in comments broadcast by Dutch television station NOS.
Geert Wilders' anti-Islam Freedom Party, the coalition's chief ally in parliament, had opposed the proposed Afghanistan mission, as did Labour, the largest opposition party.
Losing the parliamentary vote would have been a blow for Rutte ahead of provincial elections on March 2 as these help determine the make-up of the Dutch Senate.
"The mission itself is very small but politically it's symbolic. It's a very important issue because it is the main sign of being pro-American, pro-Atlantic," said Andre Krouwel, a political scientist at VU University Amsterdam.
"It shows the coalition is very stable because they can form alternative alliances with other parties on different issues."
Rutte eventually convinced three small opposition parties, the left-leaning Greens, Christian Union and Democrat 66, to support the deployment, personally guaranteeing he would keep the mission within its agreed limits.
"The reason is not America. The reason is not a seat at the G20," Rutte told MPs. "It is not exclusively a rational decision ... you have to feel it.
"This is a mission I also want. I guarantee the agreements we've made. I guarantee I will be honest with you about the things that don't go right even if that will have consequences."
Polls show a majority of voters are opposed to the mission.
GOVERNMENT FALL
The previous government in the Netherlands fell a year ago over whether to pull troops out of Afghanistan, and within months they were brought home.
More than 20 Dutch soldiers were killed in the deployment. The Netherlands was one of the first NATO countries to send its troops to the dangerous south. [ID:nLDE70Q0S0]
To gain backing for the new mission, Foreign Minister Uri Rosenthal assured lawmakers the government would obtain a firm promise from the Afghan government that police recruits trained by the Dutch would not be used in military operations.
"It seems the minority government is able to deal with the opposition and obviously this is a success for them, it means it is more stable," said Charles Kalshoven, chief economist at ING.
Germany's ruling centre-right coalition on Friday voted to extend the country's unpopular Afhan deployment by a year, with a new mandate that for the first time proposes a date for starting troop withdrawals.
From the end of 2011, the army is due to begin pulling troops out of Afghanistan. Germany has set no fixed deadline for a complete withdrawal, and has said it will continue to provide support after a NATO withdrawal planned for 2014.
Foreign Minister Guido Westerwelle said the deployment was needed to protect Germany from terrorism.
"However, the key point is that we cannot allow this deployment to last indefinitely," Westerwelle said. [ID:nLDE70R0N0] (Additional reporting by Sara Webb and Greg Roumeliotis; editing by Andrew Roche)
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