Inventories of homes for sale for over one million rose above 30,000 nationally last week according to the Institute for Luxury Home Marketing’s weekly housing report. Average days on market for higher end homes has slowly risen since the summer to each 165 days last week, still far below the national average of 292 days on market for all listings in January reported by Realtor.com.

New luxury listings are entering the market at a rate of about 1600 properties a week and a third, 34 percent, of all luxury homes on the market have reduced their prices. Average prices in the luxury category have held steady through the fall, at just above one million.

Slowest markets for sales are Philadelphia (244 days on market), Chicago (233 DOM), Miami (230), Baltimore (224 DOM), New York (208 DOM) and Detroit (205 DOM).

“The ILHM National market is currently quite strongly in the Buyer’s Marketz one (below 30). The Market Action Index stands at 13. With several months of inventory available at the current sales rate, luxury buyers should find ample choice,” reported the Institute, whose index is maintained by Altos Research.

Yesterday DataQuick reported luxury sales rose 18.6 percent last year after four consecutive years of decline.

The San Jose/Sunnyvale/Santa Clara, Calif., region posted the highest change in home sales more than $1 million, up 27.4 percent compared to 2009, followed by Riverside/San Bernardino/Ontario, Calif., (up 27.1 percent) and the New York/Northern New Jersey/Long Island MSA (up 24.7 percent). Almost 300 homes costing $5 million or more sold around Los Angeles/Long Beach/Santa Ana, Calif.