Maryland lost its ability to give unemployed workers an extra 13 weeks of unemployment aid yesterday when the state failed to meet tightened federal eligibility standards. The shut-off of extended benefits means nearly 11,000 unemployed Maryland workers will lose all benefits after July 31 and countless thousands more will be ineligible to receive aid for another 14 weeks even if the state's unemployment rate skyrockets.

Unemployment benefit problems also cropped up in the District of Columbia when the City Council voted yesterday to continue emergency belt-tightening measures in an attempt to erase a huge unemployment fund debt. Currently, the District owes the federal government $42 million on a loan taken in 1979 to keep the city's jobless aid program afloat. If the debt is not repaid by Sept. 30, the city faces stiff interest penalties enacted by a budget-minded Congress last year.

The two separate unemployment benefit problems highlight the difficulties states are having in working under stricter federal requirements while providing benefits to a growing force of jobless workers.

Maryland had been one of four states teetering on the edge of losing extended jobless benefits before it dropped under the federal threshhold yesterday.

The District is joined by Puerto Rico and 16 states in seeking federal aid to furnish unemployment funds.

In these jurisdictions, more has been paid out to jobless workers than was collected in unemployment taxes from employers.

Maryland lost its ability to extend unemployment benefits because it did not meet a complex formula set by Congress last summer. The federal government requires a state to show a certain ratio of unemployed to the state's entire work force.

Under the formula, Maryland's unemployment rate seemed to have dropped considerably since the state first lengthened unemployment benefits in February. Maryland Employment Security officials, however, say Maryland's true unemployment rate is poorly reflected under the formula because the federal government does not include as unemployed those workers who have exhausted their jobless benefit allowance of 39 weeks. Unemployed workers who already are receiving extended benefits also are not included in the federal formula.

According to Curtis Kane, director of the Maryland Employment Security Administration, the federal formula means that states that have many workers receiving extended benefits and who are jobless longer have a difficult time remaining eligible to pay the benefits.

Now that Maryland has lost that eligibility, the program cannot be reinstituted until a 13-week grace period has passed. But before Maryland can wait out the grace period, a Reagan administration plan to toughen the federal formula will go into effect. Under the Reagan plan, which takes effect Sept. 26, unemployment rates must jump another percentage point before a state is eligible to extend benefits. State officials say it is unlikely that Maryland's unemployment will be high enough to qualify under the new formula.

A distinctly different unemployment problem was tackled yesterday by the D.C. City Council. Because the number of unemployed workers far outstripped revenues raised from unemployment taxes to employers, many state-level governments have found themselves strapped for benefit funds.

In the past, states have relied on federal loans. But stiff interest penalties imposed by the federal government in April have changed this arrangement.

To avoid the high interest charges, the City Council voted to continue the tighter restrictions on issuing unemployment benefits that were first enacted as an emergency measure last December. With the restrictions, the District will make it more difficult for workers who voluntarily quit a job to receive compensation. The measure also keeps a ceiling on benefits of $206 a week and maintains a higher unemployment insurance tax rate for employers.

The District, which still has the highest individual unemployment benefits in the country, had intended to raise benefits to $222 a week before the interest penalties forced a change in plan. According to Employment Services officials in D.C., the city will avoid federal penalties by making changes like the ones approved yesterday.

D.C. officials also say the city should be able to pay off the federal loan quickly provided there is not another downturn in the economy. But if employment figures stagnate or reverse from their current slight improvement, city officials say the District's jobless fund could face another crisis and could possibly need another federal loan to survive.