FRANKFURT/LONDON (Reuters) - A report that Deutsche Bank DBKGn.DE was close to a cut-price settlement with U.S. authorities over the sale of toxic mortgage bonds helped to fuel a recovery in its shares on Friday after its chief executive said the group remained stable.

Deutsche, which is Germany’s largest bank and employs around 100,000 people, has been engulfed by crisis after being handed the demand for up to $14 billion earlier in September by the Department of Justice (DOJ) for misselling mortgage-backed securities before the financial crisis.

Deutsche shares, which hit a record low earlier on Friday, extended their recovery after the AFP news agency said the bank was near to a settlement for $5.4 billion. Deutsche and the German finance ministry declined to comment on the report.

The bank is fighting the fine but would have to turn to investors for more money if it is imposed in full. The German government this week denied a newspaper report that it was working on a rescue plan for the bank.

Worries over a major bank in Europe’s largest economy and talk of a government rescue have stirred painful memories of the 2007-2009 financial crisis and sent tremors through global markets.

Chief Executive John Cryan had tried to rally staff with a letter addressing reports of the departure of a few hedge fund clients, hitting out at “forces” that wanted to weaken trust in the bank.

People familiar with the matter had earlier told Reuters that one large hedge fund in Asia had pulled out collateral from Deutsche amounting to $50 million in the last two days, while other sources said this had happened elsewhere, albeit on a small scale.

Cryan sought to put the moves into perspective.

“We should look at the complete picture,” Cryan said in the letter to the bank’s workers, adding that Deutsche had more than 20 million customers and reserves of more than 215 billion euros.

“We are and remain a strong Deutsche Bank.”

SHARES SEESAW

Deutsche shares were volatile again, initially falling around 8 percent in Frankfurt to a record low below 10 euros before bouncing back to close six percent higher at 11.57. The bank's U.S.-listed shares DB.N were up 13.7 percent at $13.05 in heavy midday trading in New York.

The shares have lost half their value this year and the bank’s market capitalization has fallen to around 15 billion euros ($16.8 billion).

A statue is seen next to the logo of Germany's Deutsche Bank in Frankfurt, Germany, January 26, 2016. REUTERS/Kai Pfaffenbach/File Photo

Trading volume in Deutsche’s debt has more than doubled this week and soared 15-fold in a month as investors rushed to offload the troubled German lender’s bonds.

Deutsche is much smaller than Wall Street rivals such as JPMorgan JPM.N and Citigroup C.N .

But it has significant trading relationships with all of the world’s largest finance houses and the International Monetary Fund this year identified it as a bigger potential risk to the wider financial system than any other global bank.

Following the financial crisis, banks are now required to have plans showing how they would respond to a major market shock, with improved controls on liquidity. Regulators also draw up plans on how lenders could be smoothly closed down in the event of impending failure.

Italy, whose banks have their own troubles caused by soured loans, called for swift action on Deutsche.

“Just like the problem of bad bank loans must be solved within a reasonable time frame, so it should be for Deutsche Bank’s problems,” Economy Minister Pier Carlo Padoan told Italian daily La Stampa.

With Germany facing elections next year, there is little political appetite for helping a group disliked by many Germans because of its pursuit of investment banking abroad that resulted in billions of euros of penalties for wrongdoing.

However, the German government faces a delicate balancing act with a deeper crisis for Deutsche Bank potentially spilling over into its economy.

The problems of Deutsche, once Germany’s flagship on Wall Street, are awkward for Berlin, which has berated many euro zone peers for economic mismanagement and pushed for countries such as Ireland and Greece to cope with their banking problems alone.

Dutch finance minister Jeroen Dijsselbloem, who chairs meetings of euro zone finance ministers, said on Friday that Deutsche Bank must survive “on its own”, without assistance from the German state.

German banks have found their profits squeezed by the European Central Bank’s ultra-low interest rates and Commerzbank, the country’s second largest lender, is cutting almost 10,000 jobs.