* German two-year yields drop to minus 0.70 percent

* Finland 10-year yields below zero for first time

* Deutsche Bank stock drops 10 pct in two days

* Volkswagen, Commerzbank add to German woes (Adds quote, adds details on Spain and NordLB, updates prices)

By John Geddie and Abhinav Ramnarayan

LONDON, Sept 27 (Reuters) - Germany's short-term government borrowing costs hit a record low on Tuesday, as did shares in the country's biggest lender Deutsche Bank, on investor concern about the health of the financial industry in Europe's largest economy.

A broad rally in the euro zone's top-rated bonds, seen as a safe haven in times of stress, also saw Finland become the third euro area member to see its 10-year yields drop below zero, while the bloc's stock markets gave up early gains.

In other bad news for the German economy, Volkswagen's shares slumped on a report that the U.S. government was assessing how big a criminal fine it could impose on the carmaker without putting it out of business and Germany's second biggest lender Commerzbank announced 9,000 job cuts.

But Deutsche Bank, whose stock has shed more than 10 percent in the last two days and over 50 percent so far this year, is the focus of concerns after a media report said it had requested Berlin's help with a demand for $14 billion from the U.S. government to settle claims it mis-sold mortgage-backed securities. Deutsche denied the report.

"Deutsche is a natural suspect for the move in the Bund yields," said Ciaran O'Hagan, strategist at Societe Generale.

"Germany is a core-rated country, and worries over Deutsche will still benefit Bunds...even if the concerns about Deutsche hurt Germany Inc."

German two-year bond yields fell to a record low of minus 0.711 percent, down 3 basis points on the day, while 10-year yields dropped 4 bps to minus 0.15 percent at one stage, their lowest since Aug. 15.

"There's a risk-off mood in the market prompted by the Deutsche Bank worries, and you can see that mood reflected across asset swap spreads, and an underperformance of peripheral bonds," said Benjamin Schroeder, senior rates strategist at ING.

That cautious mood prompted German lender NordLB to shelve a planned bond issue on Tuesday as it struggled to find demand amid broader concerns about the country's banking sector.

Elsewhere, Finland's 10-year yield fell into negative territory for the first time, down 2.5 basis points at minus 0.015 percent.

That means investors are now willing to pay Finland to lend to it for 10 years, a boon so far only granted to Germany and the Netherlands within the single currency bloc, and only to a handful of countries globally.

Spain's 10-year bond yield also hit a fresh low of 0.89 percent, though it edged back up to 0.91 percent by 1500 GMT, down 1.8 bps on the day.

Aside from Germany's woes, strategists pointed to upcoming U.S. elections and a referendum on constitutional reform in Italy that could jolt markets in the coming months and increase demand for top-rated bonds.

Investors in Italian bonds appeared to take a crumb of comfort for the government's decision on Monday to push back the date for the referendum to December, a move that may give Prime Minister Matteo Renzi time to win over sceptical voters.

(Additional reporting by Dhara Ranasinghe; Editing by Raissa Kasolowsky and Hugh Lawson)