The bank also acknowledged for the first time that a small number of its employees - but no executive board member - had been involved in the Libor interest-rate rigging scandal that has rocked the financial world.
In view of the current difficult environment, Deutsche Bank said it would "reduce headcount predominantly outside of Germany by approximately 1,900 positions."
These measures were expected to contribute savings of approximately €350 million of an overall cost-cutting target of €3.0 billion, the statement said.
The news sent Deutsche Bank shares soaring on the Frankfurt stock exchange, where they were showing a gain of 2.39 percent at €25.44 in a slightly firmer market.
Earlier, Deutsche Bank had announced that its net profit fell to €661 million in the second quarter of the year, from €1.2 billion a year earlier, and revenues declined 6.0 percent to €8.0 billion.
The group's performance "was impacted by a volatile environment. The European sovereign debt crisis continues to weigh on investor confidence and client activity across the bank," said co-chief executives Jürgen Fitschen and Anshu Jain.
The net profit figure was lower than a provisional estimate of €700 million which had already disappointed analysts when it was released last week.
The fall in profits is fuelling concern whether Deutsche Bank can meet the EU's more stringent capital requirements without issuing new shares to raise additional funds.
But the bank said it had "always maintained, and currently maintains capital ratios which are comfortably above all regulatory thresholds and plans to continue to do so."
Deutsche Bank said its core Tier 1 capital ratio - a key measure of financial health - stood at 10.2 percent at the end of the second quarter, up from 10 percent three months earlier and above the 9.0-percent minimum required by regulators.
The firm said it would only seek a capital increase as last resort. "The bank further aims to continue to grow this ratio through the rest of 2013 and beyond. The bank aims to apply all capital levers at its disposal before considering raising equity from investors," Deutsche Bank said.
In a letter to staff, Deutsche Bank's supervisory board chief Paul Achleitner also confirmed for the first time that an internal investigation has been launched into the Libor affair.
"As per the current status of investigations, we can say that no current or former member of the management board had any inappropriate involvement," Achleitner wrote in the letter, a copy of which was obtained by AFP.
"It has also found that a limited number of employees, acting on their own initiative, engaged in conduct that falls short of the bank's standards, and action has been taken accordingly."
Co-CEO Jain came under the spotlight over his possible role in the rigging of the Libor interbank rate which underpins rates on a wide range of lending from mortgages to credit cards.
Before his appointment in June, Jain headed Deutsche Bank's investment banking operations in London where one of its traders was allegedly involved in the scam.
And while it was Jain himself who ordered an internal probe into the affair as far back as 2010, the investigation was initially not pursued with particular intensity, according to recent newspaper reports.
The affair was also one of the reasons Jain's predecessor Josef Ackermann did not want the 49-year-old investment banker to replace him, the business newspaper Handelslbatt reported recently.
British paper The Financial Times said a Deutsche Bank trader had been formally named as a suspect in the Libor probe.
While Deutsche Bank declined to comment, it did tell AFP that the trader concerned no longer worked for the bank.
British bank Barclays has already been fined £290 million (€360 million) as part of a probe into the scandal by British and US authorities.