WASHINGTON (Reuters) - U.S. single-family home prices increased at a steady clip in April, but momentum could slow as higher borrowing costs weigh on demand for housing, contributing to a rise in supply.

House prices rose 0.2% month-on-month after being unchanged in March, the Federal Housing Finance Agency said on Tuesday. In the 12 months through April house prices increased 6.3% after advancing 6.7% in March.

"House prices continued to rise in April," said Anju Vajja, deputy director for FHFA's Division of Research and Statistics. "However, the appreciation rate slowed in April amid a slight rise in both mortgage rates and housing inventory. The housing market in general began to show some signs of normalization."

The National Association of Realtors reported last week that existing home sales decreased for a third straight month in May as a resurgence in mortgage rates combined with higher prices to reduce affordability. Housing inventory jumped last month to the highest level in nearly two years.

The average rate on the popular 30-year fixed mortgage hit a six-month high of 7.22% in early May, data from mortgage finance agency Freddie Mac showed. Though it has since retreated to 6.87% last week, the rate remains above the 6.67% average during the same period last year.

The housing market has taken a step-back since residential investment posted double-digit growth in the first quarter.

All nine census regions recorded annual house price gains in April, with hefty increases in New England and Middle Atlantic.