About 493,000 jobless Americans filed first-time claims for unemployment compensation insurance in the week ending March 12, compared with 501,000 the previous week, the Labor Department said yesterday.

Also yesterday, the economic reporting firm F. W. Dodge reported that contracting for new construction declined in February.

The weekly jobless claims report showed 6,115,500 unemployed people were getting benefit checks paid through a variety of programs in the week ending March 5, down 317,100 from the previous week.

The total number of people drawing regular benefits under state-run programs also declined--from 3,995,000 to 3,915,000--in the week ending March 5, the agency said.

It said the nation's insured unemployment rate--the proportion of the civilian labor force getting jobless benefits--dropped 0.1 percentage point from 4.6 to 4.5 percent.

Meanwhile, F. W. Dodge reported that contracting for new construction fell 6 percent to $11.3 billion in February. That decline followed a strong January gain, said the division of McGraw-Hill Inc.

F. W. Dodge said its seasonally adjusted index recorded 119 in February, compared with 127 the previous month. The index uses a basis of 100 equaling the value of construction contracts in 1977.

Dodge chief economist George A. Christie said the February decline was not a sign that the construction industry's recovery may be stalling. "Erratic behavior of construction activity is typical for the winter quarter when minor month-to-month variation is less important than the average level of contracting over several months," he said.

So far this year, Christie said, the seasonally adjusted rate of contracting has averaged 3 percent higher than the last quarter of 1982.

F. W. Dodge said that contracts for non-residential building in February fell 6 percent to $4.2 billion; contracting for residential building dipped 7 percent to $4.8 billion, while non-building construction rose 7 percent to $2.3 billion.