Henry Kravis’ large ambitions for his firm will have to wait.

In a letter sent yesterday to the SEC, KKR & Co. said it will not go forward with a highly anticipated $500 million stock sale “due to unfavorable market conditions.”

In May the company said it was raising the capital to expand further into areas beyond its private-equity business.

The cancellation comes at KKR shares have fallen more than 10 percent since they started trading last month on the NYSE at $10.50. Shares closed yesterday at $9.89, up 3 cents.