Hawaii’s unemployment rate fell to 6.3 percent in April from 6.4 percent in March, reaching its lowest level in more than three years, the state reported Thursday.

The state’s seasonally adjusted jobless rate has been improving slowly after peaking at 7.1 percent in the summer of 2009 amid one of the worst economic downturns since statehood.

Most economists expect further improvement in the state’s job market will be gradual as the economy slowly strengthens. The University of Hawaii Economic Research Organization is forecasting the unemployment rate will average 6.1 percent this year and 5.4 percent in 2013.

April’s 6.3 percent jobless rate was the lowest since January 2009 when it was 6.1 percent.

There were 41,350 people looking for work in Hawaii in April, according to the state Department of Labor and Industrial Relations. That was down from 42,300 in March and 43,500 in April 2011.

While job growth has been slow in recent years, the deterioration of the job market after the 2008-2009 recession was rapid. The jobless rate nearly tripled in a span of two years, and the number of people filing for unemployment insurance soared from fewer than 1,000 a week to more than 3,000 a week.

However, unemployment claims have been trending lower over the past year. There were 1,707 claims filed for the week ending May 12, down 31.1 percent from the same week a year ago.

Nationally the unemployment rate fell to 8.1 percent in April from 8.2 percent in March.

The state and national jobs data are adjusted for seasonal variations, such as temporary hiring during the holiday shopping season.

County jobless rates are not seasonally adjusted. The rate for Hono­lulu fell to 5.3 percent in April from 5.7 percent in March. In Maui County the rate dropped to 6.5 percent from 7.1 percent. In Kauai County it fell to 7.7 percent from 8.1 percent, and in Hawaii County it declined to 8.7 percent from 9.2 percent.

The unemployment rate is based largely on a telephone survey of households. A separate survey of businesses showed that the number of nonagricultural jobs rose to 600,900 in April, a 4,600 net increase from March.

In the private sector, the trade, transportation and utilities sector gained 500 jobs, while financial activities and other services added 400 positions apiece. Education and health services lost 500 jobs, while employment in the construction industry dropped by 200.