* Swiss Re net income rises to $802 mln in Q2
* Says July renewal premium volume up 8 pct
* CEO sees further softening in insurance market (Adds earnings details, industry context)
ZURICH, Aug 6 Swiss Re, the world's second-largest reinsurer, said on Wednesday its net profit rose less than expected in the second quarter, as the firm's chief executive warned he saw prices weakening further in the insurance industry.
"We see the insurance market generally softening," Chief Executive Michel Lies said in a statement.
Ultra-low interest rates since the financial crisis have attracted investors such as pension funds, known as "alternative capital", to pour money into the reinsurance market in search of higher returns, putting pressure on prices.
However, the Zurich-based firm said policy renewals in the Americas, Australia and New Zealand had been successful in July, with premium volume up by 8 percent.
Other than a storm in early June that caused around $900 million in damage in Germany, reinsurers have seen little in the way of big disaster claims in recent months.
That helped Swiss Re's second-quarter net profit rise 2 percent to $802 million from $786 million a year earlier.
Still, that was below an expected quarterly net profit of $897 million, according to the average of six estimates in a Reuters poll of banks and brokerages. (Reporting by Alice Baghdjian; Editing by Kenneth Maxwell)