John Cryan told them the bank had become the object of “hefty speculation” and that “new rumours” were causing the share price to fall.
Deutsche’s shares hit new lows on Friday as confidence in the bank continued to falter.
But Mr Cryan said the bank’s reserves and profits underlined its strength.
He pointed out that Deutsche had €215bn in reserves and made €1bn in profits for the last six month. At no point in the last 20 years had Deutsche been as strong as it is now, Mr Cryan insisted.
“The release of the memo… seems to have taken the edge off of the German company’s dramatic” share price decline, said SpreadEx analyst Connor Campbell.
Deutsche shares were down 5% at midday, having fallen 9% earlier.
That followed a big fall overnight in the bank’s Wall Street-listed shares, a drop sparked by reports that some hedge funds had withdrawn money from the bank.
But Deutsche Bank is under the most pressure of any bank since the financial crisis.
Investors are increasingly worried about the financial health of the bank, which faces a $14bn fine in the US for mis-selling mortgage-backed bonds before the financial crisis of 2008.
The bank’s shares, worth about €10.4 on Friday, have been falling steadily from a recent high of €27.80 last November. But at their peak in May 2007, before the start of the banking crisis, the shares were valued at almost €100.
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Deutsche’s woes hit bank shares across Europe. German rival Commerzbank was down about 6%, while the shares in UK, Swiss, French and Italian banks also suffered.
In Italy, Economy Minister Pier Carlo Padoan told La Stampa newspaper that it was in everyone’s interest “to look for solutions that must then be carefully handled”.
But the German government’s position is not clear.
Although a newspaper report earlier this week suggested the German government had made some provisional plans to rescue Deutsche, this would be politically unpopular.
Eckhardt Rehberg, parliamentary budget spokesman for Chancellor Angela Merkel’s conservative CDU party, told Reuters: “At the present time, I would rule out any capital help. That would not be the right way to go.”
Deutsche Bank made a net loss of €6.8bn last year and has embarked on a round of hefty cost-cutting that includes shedding 15% of its 100,000-strong global workforce.
Like most of the world’s leading banks, Deutsche Bank has been embroiled in the major banking scandals of recent years, including rigging interest rates.