The department said project starts rose 7 percent above February's revised figure of 968,000 starts on a seasonally adjusted annual rate, reaching an annual rate of 1,036,000.
The figure has not topped 1 million since June 2008, when it stood at 1,046,000.
The rate of housing starts for March are also 46.7 percent above March 2012 when project starts came to 706,000.
At 902,000, the number of permits issued for private projects was 3.9 percent below February's revised rate of 939,000, although it is 17.3 percent above March 2012 when 769,000 permits were issued.
Residential project completions came to an annual rate of 800,000 in March on a seasonally adjusted basis, 11 percent higher than February's revised rate of 721,000 and 36.3 percent above March 2012, when the rate for completions was 587,000, commerce said in a release issued with the Department of Housing and Urban Development.