* Defaults rise, cures decline on insured mortgages

* Deterioration slows from prior month

* Weakness follows end of foreclosure moratoriums

NEW YORK, July 31 (Reuters) - Defaults on privately insured U.S. mortgages increased and the number brought up to date fell in June for a second straight month, reflecting further pressure in the nation's housing market, though the pace of deterioration slowed.

The Mortgage Insurance Companies of America, a trade group, said 88,362 insured borrowers were at least 60 days late on payments in June, up less than 1 percent from May and up 30 percent from a year earlier. Late payments often foreshadow foreclosure. The number had risen 8 percent in May.

Mortgages brought up to date totaled just 51,908, down 1 percent from May and the fewest since January, but up 20 percent from a year earlier. The month-over-month decline had been 10 percent in May.

Private mortgage insurance lets people buy homes with down payments of less than 20 percent, and guarantees that lenders will be repaid even if borrowers default. Insurance in force totaled $915.1 billion in May, the trade group said.

The industry has been tightening its standards after struggling with losses from having backed subprime and other risky mortgages, which have eaten into capital.

While most major U.S. home loan providers adopted mortgage modification programs in the last year to keep borrowers in their homes, many foreclosure moratoriums expired in March.