MADRID, March 7 (Reuters) - Hungary's Ganz Mavag (Magyar Vagon) has launched a 619 million euro ($677 million) public tender offer for all the shares of Spanish train maker Talgo , a deal set to face tough scrutiny in Madrid.

The consortium, which includes Hungarian state fund Corvinus, is offering 5 euros per share in cash, it said on Thursday in a filing to the Madrid stock market regulator.

The Spanish government has already said that it will look carefully at the deal, since it considers Talgo a strategic asset.

"Talgo is a company that we consider strategic in the country because it plays a fundamental role in rail mobility," Industry Minister Jordi Hereu said earlier on Thursday.

"We are going to work on it, we are going to defend this industrial project," he said.

Talgo had a market value of 525 million euros at closing on Wednesday.

The train maker, whose main shareholder is private equity fund Trilantic, was listed on the Madrid stock market in May 2015 at a valuation of 1.25 billion euros.

($1 = 0.9147 euros) (Reporting by Pietro Lombardi, editing by Inti Landauro and David Latona)