Construction continued to rise in May, increasing by 3 percent to an estimated $198.6 billion from $193 billion in April, the Commerce Department announced yesterday.

The largest seasonally adjusted upturn was an 8 percent gain in public construction to $44.8 billion. Private nonresidential building construction rose 5 percent to $33.2 billion, while private residential building rose only slightly from $90.1 billion in April $91.5 billion.

The average annual rate increase for March, April and May was 9 percent higher and for the previous three months and 13 percent above the total for March through May in 1977, the Commerce Department said.

A Census Bureau breakdown showed that both office building and other commercial construction rose 11 percent above the April level in May. This upturn can be interpreted in Washington and other large urban area as continued evidence of a boom of varied office-type enterprises as well as in new shopping facilities in cities and suburbs.

In this metropolitan area, more than a dozen large office buildings or complexes with shops and other facilities are under way to meet a rising demand for space by private tenants, many of whom are associations and accountants.

The most significant upturn in public construction activity was 26 percent in highways and streets to $10.7 billion. This reflects the need for roads to serve the housing market that has been at a high level for 18 months and repairs of roads damaged by two consecutive frigid winters.