WASHINGTON, Oct 25 (Reuters) - Sales of new U.S. homes crept up to a record level in September, the government said on Friday, as the lowest mortgage rates since the 1960s helped keep at least one sector of the economy shining.

Sales of new single-family houses climbed 0.4 percent to a seasonally adjusted annual rate of 1.021 million units last month from an upwardly revised 1.017 million unit pace in August, the Commerce Department said.

The sales performance was stronger than economists had expected. Wall Street had looked for the sales rate to slip to 991,000 units from the previously reported 996,000 homes rate in August.

The housing market has continued to thrive, helped by the lowest mortgages rates in over a generation, even as much of the rest of the economy sputters in a weak recovery.

A separate report on Friday showed existing homes sales were strong last month as well. The National Association of Realtors said existing home sales rose 1.9 percent in September to a 5.40 million unit annual rate. New home sales were strong in the Northeast, rising 94.2 percent to their highest level since January 1997, and in the West, where activity increased 2.2 percent.

That strength more than offset weakness in the South and Midwest. In the South, where the lion's share of home sales take place, sales fell 8.6 percent, and in the Midwest sales were off 4.1 percent.

Despite September's sales record, the inventory of homes on the market rose to a 4.0 months' supply at last month's sales pace. That's because the number of homes on the market at month's end moved up to 332,000 -- the highest level since August 1996 -- from 330,000 a month earlier.

The department said the median sales price of new single-family houses, the level at which half of the homes sold for more and half sold for less, rose to $176,300 last month from $174,700 in August.