Denmark pushes to widen probe into multi-billion-euro tax fraud

* Denmark tricked into paying $2 billion tax rebates

* Danish minister asks for banks to provide information

* Germany and other states investigate dividend stripping

COPENHAGEN/FRANKFURT, Nov 2 (Reuters) - Denmark is widening its investigation of a massive stock trading scam, as the state attempts to recover $2 billion of tax reclaims it was tricked into paying.

The country's tax minister has asked the financial regulator to gather information from some large banks to help with the inquiry, as a series of probes around Europe into so-called dividend stripping gathers pace.

Danish authorities have already subpoenaed more than 420 companies and people they suspect of involvement, freezing hundreds of millions of euros of assets around the globe.

Its tax authorities say they lost $2 billion, while Germany estimates it was tricked out of more than 5 billion euros by a similar "cum-ex" method. Other countries, such as Austria and Belgium, were also hit.

The schemes typically involved trading company shares rapidly around a syndicate of banks, investors and hedge funds to create the impression of numerous owners - each entitled to a tax rebate. It cost some countries billions of euros when illict rebates were granted.

Tax Minister Karsten Lauritzen has asked for three banks, Danske Bank, Nordea and SEB, to contribute information to the investigation. "I'm not convinced the banks have lived up to their social responsibilities," Lauritzen told journalists on Thursday.

On Friday, those banks expressed willingness to help with the investigation but stressed they had not been involved in wrongdoing.

The country's financial watchdog told Reuters it would discuss the minister's request with the tax authorities "as soon as possible".

A spokesman for Danske said there had been no fraud involving the bank but that it would contribute "documentation and knowledge" to the investigation.

Nordea said it would also help, although it had not been involved in Danish cum-ex trading. An SEB spokesman said there was no question of it being involved in a fraud.

European politicians have called for action to tackle dividend stripping after Reuters and other media revealed the trading schemes that cost taxpayers billions of euros.

Reuters spoke to bankers, officials and people directly involved in the probe and reviewed thousands of pages of internal bank files, correspondence and legal papers obtained as part of a European media investigation called the "cum-ex files", coordinated by non-profit newsroom Correctiv.

In what is Germany's biggest post-war fraud investigation, prosecutors in Cologne are investigating banks involved in the trades, which secured illicit double tax rebates on dividend payouts.

Germany changed and clarified the law in 2007, 2009 and 2012 to stamp out the practice.

Olaf Scholz, Germany's finance minister, has said that any tax reclaimed illicitly under dividend stripping schemes would have to be paid back.

The discovery of the trades in Germany and Denmark has prompted other countries, including Austria and Belgium, to open their own investigations. They have discovered that they were also affected, but on a far smaller scale. (Additional reporting by Johann Ahlander in Stockholm; editing by Andrew Roche)