The Labor Department announced yesterday that nine states shortly will be dropped from the extended benefits program of the federal-state unemployment insurance system as a result of new eligibility standards proposed by President Reagan and enacted by Congress last year that take effect this month.

Fifteen other states, whose unemployment rates are high enough to satisfy the new standards, will continue to be eligible for the extended benefits program.

The nine states being dropped are Alaska, Arizona, California, Louisiana, Montana, Nevada, North Carolina, Rhode Island and Utah.

Workers in those states will lose eligibility starting Saturday for the extra 13 weeks of extended benefits that are available in high-unemployment states after a jobless person uses up the initial 26 weeks of state benefits. About 135,000 unemployed persons in the nine states are now drawing the extra 13 weeks.

Some of these workers, plus others going off regular benefits in the next few months, will be able to shift from the extended benefits program to a special temporary federal program enacted last summer that provides up to 10 weeks of added benefits for workers who exhaust regular benefits.

But they won't be as well off. Under the old rules, they could have received 26 weeks of basic benefits, plus 13 weeks of federal-state extended benefits, and in addition, the 10 weeks of special federal benefits. As a result of the change announced yesterday, many workers will get only the initial 26 plus the 10 weeks from the special program, losing the entire 13 weeks of federal-state extended benefits or a part of the 13 weeks.

The added 13 weeks of federal-state financed extended benefits until this month were available in states that over a 13-week period had an "insured unemployment" rate of 4 percent with a 20 percent increase over the prior two years, or alternatively a 5 percent insured rate. The 1981 change upped these figures to 5 percent with a 20 percent increase, or 6 percent, effective this month, causing the nine states to drop out.