A special national commission yesterday recommended a major overhaul of the nation's unemployment insurance system, including raising jobless benefits in many states and establishing a federal "reinsurance" program to share the costs of unemployment compensation.

The commission's recommendations are bound to cause considerable controversy. Business and employer groups and many states with low benefits and low unemployment taxes have opposed all move to set minimum benefit standards or share costs.

The National Commission on Unemployment Compensation, headed by Wilbur J. Cohen, former secretary of Health, Education and Welfare, outlined recommendations after a nearly three-year study of the federal-state unemployment insurance system set up by the 1935 Social Security Act.

Under the existing law, each state sets its own basic benefits and finances most of the cost.

Critics of the system complain that some states keep benefits too low. The maximum ranges from $90 a week in Mississippi to $197 in Massachusetts. As of Jan. 6, the District paid up to $181 a week, Maryland up to $106 and Virginia $122.

There are also complaints that the system is unfair to states that are hit with high unemployment when the nation's economy runs into a recession. To pay for unemployment claims, states have to raise business taxes. The high taxes discourage industrial growth and causes some companies to move, resulting in more unemployment, still higher traxes and a narrower tax base.

The commission's recommendations are:

Require every state to pay basic benefits equal to at least half the worker's previous average weekly wage, provided this doesn't exceed two-thirds of the average weekly wage in the state.

Set up a permanent, federally financed system to guarantee workers up to 26 additional weeks of benefits on top of the basic 39 weeks of unemloyment compensation. The extra six months of benefits would be made available during periods of severe, prolonged unemployment.

Set up a "reinsurance" system by diverting one-tenth of one percent of the federal unemployment tax into a fund to help state with high cost due to recessions.

Strengthen future financing by raising the amount of wages on which employers pay unemployment taxes to 65 percent of the national average wage by 1989. Taxes are collected now only on the first $6,000 of each employe's earnings.