Credit Suisse Group AG Chief Executive Thomas Gottstein said a report that the bank could be taken over by State Street Corp. was “really stupid” and that the lender can repair itself.

The CEO is under pressure from investors to show that the bank has a credible strategy after a spate of scandals and financial losses. On Wednesday, Credit Suisse warned it is likely to report its third consecutive quarterly loss because of a sharp fall in investment-banking deals such as companies raising new stock and bonds. It said it would speed up cost-cutting plans.

Mr. Gottstein dismissed a report on a Swiss finance blog on Wednesday about a deal with State Street. “My father once gave me advice: For really stupid questions, you better don’t comment at all,” he told investors at a Goldman Sachs Group Inc. conference Thursday. 

On Thursday, State Street also denied the news report. “State Street is not pursuing an acquisition of, or any other business combination with, Credit Suisse,” a spokesman said in a statement. “There is no basis to the continuing market rumors.”

The talk of a deal initially sent Credit Suisse’s share price up nearly 10%, but it has since retreated and traded close to all-time lows.

Mr. Gottstein also said the bank isn’t considering a joint venture to spin off its asset-management arm or any other strategic upheaval to its four core divisions: wealth management, investment banking, asset management and its Swiss universal bank.

The bank’s asset-management arm, a mix of Credit Suisse funds and partnerships with other fund managers, is seen as an acquisition target for rivals. Analysts say a sale would be a way to raise capital to put into wealth management and for Credit Suisse to shore up its balance sheet, but would mean more lost revenue after closing other businesses in recent months. 

Mr. Gottstein said the bank has the firepower to fix its situation in part by cutting jobs and slowing investments. He said positions that could go were in front-line trading and banking, and in technology and other “back office” roles.

Chief Executive Thomas Gottstein said Credit Suisse has the firepower to fix its situation in part by cutting jobs and slowing investments.

Photo: Jason Alden/Bloomberg News

Mr. Gottstein said the bank would give more details on its cost-cutting plans at an investor day on June 28. He said the bank is still hiring in some areas, but is slowing down some investment plans, such as hiring more relationship managers in China. 

Credit Suisse’s future form has been uncertain since the bank lost more than $5 billion last year from the collapse of family office Archegos Capital Management. It shuffled its executive team and board and updated its strategy in November, with plans to cut up to $1.5 billion in annual costs and shift capital from investment banking to wealth management. Some investors are skeptical the plans are enough, though, and want to see more sweeping changes. 

Since the hit last year from Archegos, various suitors including U.S. banks have considered buying parts of Credit Suisse, according to people familiar with the matter. Credit Suisse has said it isn’t for sale.

In 2015, Credit Suisse exited wealth management in the U.S. in an effort to save costs, largely cutting itself off from managing the world’s biggest pool of wealth. Last year, it exited prime brokerage, a business serving hedge funds that has been lucrative for other banks.

Write to Margot Patrick at margot.patrick@wsj.com