American International Group Inc. saw double-digit rate increases in numerous lines during the second quarter, including a nearly 40% increase in cyber liability insurance rates, the insurer’s top executive said Friday.

AIG also made progress with its plan to separate its life and retirement business from its property/casualty operations during the quarter and will likely increase the size of its initial public offering for the life and retirement unit, Peter Zaffino, president and CEO of AIG, said on a second-quarter results conference call with analysts.

Global insurance rates increased 13% on an annual basis in the second quarter, he said.

North America commercial rates rose 13%, with the highest increases in excess casualty, up 20%; surplus lines casualty, up 19%; and surplus lines property, up 17%, he said.

International commercial rates also increased 13%, Mr. Zaffino said.

Across AIG’s global portfolio, the largest rate increases were in cyber liability insurance, where rates were up almost 40%, with the largest rate increases in North America, he said.

“We continue to carefully reduce cyber limits and are obtaining tighter terms and conditions to address increasing cyber loss trends, the rising threat associated with ransomware and the systemic nature of cyber risk generally,” Mr. Zaffino said.

AIG Re, the insurer’s reinsurance business, reported a more than 30% increase in net premiums written in the second quarter. U.S. property catastrophe reinsurance rate increases ranged from “mid-single digits to upwards of 25%,” Mr. Zaffino said.

Validus Re, which AIG bought in 2018, reduced its net limits in Florida by 40% at June 1 renewals, as AIG continues to reposition the business to focus on regional and nationwide insurers in the United States and increased international diversification, he said.

Meanwhile, AIG’s planned separation of its life and retirement business continues after the July announcement that it had agreed to sell a 9.9% stake in the unit to Blackstone Group Inc. for $2.2 billion. A Blackstone affiliate also agreed to buy AIG’s U.S. affordable housing portfolio for $5.1 billion.

AIG still plans an IPO for the life and retirement unit, which will likely take place in the first quarter of 2022, Mr. Zaffino said. When it announced the planned IPO last October, AIG said selling only 19.9% of the unit would preserve some foreign tax credits it benefits from.

“The gain on the sale of affordable housing, coupled with other factors, provides us with flexibility to sell down beyond 19.9% as we now expect to fully utilize our foreign tax credits in 2022,” Mr. Zaffino said.

AIG reported net income of $91 million in the second quarter, compared with a $7.94 billion loss in the same period last year, which was affected by the sale of runoff reinsurer Fortitude Group Holdings.

In its main property/casualty unit, AIG reported net written premium of $6.86 billion in the second quarter, up 23.6% compared with the 2020 period.

North America commercial lines reported $2.66 billion in net written premium, up 15.3%. New business increased 25% from the prior-year quarter, led by financial lines and surplus lines business, Mr. Zaffino said.

International commercial lines reported $2.06 billion in net premium written in the quarter, a 16.6% increase over the same period last year.

AIG reported a combined ratio of 92.5% for the quarter, compared with 106% a year earlier. Catastrophe losses were $118 million in the second quarter compared with $674 million in the prior-year quarter.