* Probe to cover years of possible failed due diligence
* ABN Amro says "this is a top priority for us"
* Shares down nearly 10% in morning trade
* Dutch finance minister: probe is "obviously worrying" (Adds background, reaction from DNB, finance minister)
AMSTERDAM, Sept 26 (Reuters) - Dutch prosecutors are investigating alleged money laundering at ABN Amro, one of the largest banks in the Netherlands, saying they suspect the lender had failed to report or probe suspicious transactions for years.
ABN Amro shares tumbled nearly 10% in early trading in Amsterdam, as the bank said it had no indication of the impact of the investigation.
The move against ABN Amro is part of a broader push by prosecutors in Europe to crack down on lax monitoring of illegal transactions via bank accounts. It was disclosed a day after German authorities raided Deutsche Bank's headquarters over a money laundering scandal at Danske Bank .
Prosecutors said they believe ABN Amro reported suspicious transactions too late or not at all over a long period, adding the bank failed to properly investigate client behaviour and did not sever ties with suspect clients in a timely fashion.
The period over which the alleged failures occurred was not disclosed.
Prosecutors said the probe was based on information provided by the Dutch central bank, which earlier this year ordered ABN to review all Dutch retail clients for possible money laundering or other criminal activities.
ABN Amro, which in August had warned of possible fines over failures in client oversight, was notified of the investigation on Wednesday but was not given further details on the scale of inquiry, said ABN spokesman Jeroen van Maarschalkerweerd.
"We have stated clearly over the past few years that we also felt we had to improve," he said.
"This is a top priority for us, we have always known we had to do things better, but we have also always been clear that an investigation such as this might occur."
KEEPING CRIMINALS OUT
Finance Minister Wopke Hoekstra said "it's extremely worrying that ABN Amro is under investigation by prosecutors" and that the government is resolved to combat laundering.
"Banks have an important gatekeeper function in keeping criminals out," he said.
With the outcome of the probe unclear, analysts turned to a record $900 million fine on fellow Dutch bank ING last year as a reference point for the penalty ABN Amro could face.
ING was fined in September last year for failing to spot criminal activities financed through its accounts, including bribery payments to foreign officials.
After that fine, the Dutch central bank said local banks were still too lax on money laundering, and should do more to stop it.
Dutch central bank spokesman Tobias Oudejans told Reuters "this investigation can be seen in light of last year's warning. We stand by this warning, and this investigation underlines that these issues have not been fully resolved yet."
Investigators last year estimated that an annual amount of around 13 billion euros ($14.2 billion) was laundered in the Netherlands over 2004-2014, equivalent to roughly 2% of GDP.
In the months following ING's fine, ABN said it had increased anti-money laundering operations at a cost of nearly 200 million euros, with a dedicated staff of more than 1,000.
ABN Amro was bailed out by the Dutch state in 2008. It was re-privatized in 2015, but the state still holds a 56% stake. ($1 = 0.9137 euros) (Additional reporting by Toby Sterling; Editing by Deepa Babington)