Construction spending shot up 1.6 percent in August, the biggest increase in four months, the government reported this week.

The Commerce Department said construction projects were being built at a seasonally adjusted annual rate of $399.6 billion in August. It was the biggest advance since a 2 percent rise in April and followed declines of 0.1 percent in July and 0.7 percent in June.

The strength last month came in part from a rebound in spending on apartment construction, which rose 6 percent to an annual rate of $24.9 billion. But even with the increase, apartment construction is still 19 percent below where it was a year ago.

In the overall residential construction area, spending rose by 1.4 percent to an annual rate of $200.6 billion. The strength came from the apartment sector as construction of single-family homes was unchanged in August. This sector has been hurt by the sharp increases in mortgage rates this year.

Nonresidential construction rose 2.6 percent in August from the July spending level to an annual rate of $85.5 billion, but still remained 6 percent below the level of a year ago.

Activity in this sector is likely to remain below last year's level because of the adverse effects of the new tax law on such investments as office construction.

In August, construction of offices was up 2.8 percent from July but activity was 10 percent below a year ago.

Construction of government projects climbed 0.9 percent to an annual rate of $74.5 billion despite the fact that the biggest government spending category, highway construction, fell 4 percent in August.

For the first eight months of the year, spending on construction projects is 1.9 percent below the total spent during the same period in 1986.