About 3,000 unemployed workers in the District of Columbia and many thousand more in Maryland and Virginia whose unemployment benefits have expired or are about to expire will be eligible for as many as 13 extra weeks of payouts under a federal program that starts Sunday.

The program extends benefits for workers in the District by five weeks and for workers in Maryland and Virginia by 13 weeks. In all three jurisdictions, employed workers, whose former employers pay quarterly unemployment insurance premiums, will be eligible for a total of 39 weeks of benefits.

A Labor Department official estimated that about 250,000 unemployed workers across the nation will be eligible for the so-called extended unemployment benefits.

The extra period of benefits was triggered when the unemployment rate among workers who employers pay unemployment insurance premiums rose above 4.5 per cent in the week ending Aug. 13.

The unemployment insurance program is a complicated blend of federal and state efforts. The first stage of unemployment benefits - 26 weeks in most states including Maryland Virginia and 34 weeks in the District - are paid for by local judisdictions from funds provided by a tax on employers.

In the recession of 1974 and 1975, Congress added an extended benefits program that kicks in on a national basis when the insured unemployment rate rises above 4.5 per cent. The federal government pays half of these benefits.

When the insured unemployment rates dipped below 4.5 per cent in early July, the extended program expired as of July 23. The rate climbed back to 4.508 per cent in the week ending Aug. 13, triggering a 13-week renewal of the program beginning Sunday.

Even if the insured unemployment rate dips below 4.5 per cent, the extended benefits remain in effect for a minimum of 13 weeks.

Most workers are eligible for unemployment insurance but not all.

Eligibility, benefits and the duration of payouts are determined by individual states. The District has the highest unemployment insurance benefits in the country.

The over-all unemployment rate which includes those who are not eligible such as farm workers and those who have used up their eligibility for benefits was 6.9 per cent in July, the federal government.

While unemployed workers in the District will be eligible for only five weeks of unemployment benefits because of the city's liberal plan, the District's unemployment insurance plan, already in debt to the federal government for $52 million to maintain payments, will fare a little better.

The federal government will pay 50 per cent of the cost of providing benefits to persons out of work for more than 26 weeks. That means that half of the payouts the District's fund would have provided to workers unemployed for more than 26 weeks and less than 34 weeks now will be absorbed by the federal government.

Twelve states and Puerto Rico did not lose extended benefits last month because their insured unemployment rates were higher than 5 per cent. Under the law, all states are eligible for the program when the national rate is higher than 4.5 per cent, but individual states qualify for the program if their rates are above 5 per cent.