Millions of Americans have run out of unemployment insurance benefits because of the ''continuing relentless march'' of unemployment, AFL-CIO president Lane Kirkland warned Congress in a drive to win an extension of jobless benefits beyond the 39 weeks most unemployed now receive.
Reacting sharply to May figures showing the unemployment rate at a new post-World War II high of 9.5 percent, Mr. Kirkland said the Bureau of Labor Statistics report ''demonstrated forcefully the need for action'' to keep long-term jobless workers from facing total economic disaster.
A bill introduced by Rep. Harold Ford (D) of Tennessee, chairman of the House subcommittee on unemployment compensation and public assistance, would add another 13 weeks of emergency benefits to bring the total to 52 weeks. (The AFL-CIO is pressing for 65 weeks but will back the bill for 52.)
In the Senate, Robert Byrd (D) of West Virginia has introduced slightly different legislation also calling for a 13-week extension.
According to AFL-CIO:
* There are currently at least 3.2 million workers who have sought jobs unsuccessfully for more than six months and have exhausted unemployment compensation rights. Federal and state rules usually allow recipients to collect benefits for 26 weeks, plus an additional 13 weeks of emergency aid contingent upon the rate of unemployment.
* Recipients of the benefits (which average from $72 to $122 a week) are not being cushioned sufficiently against hardships, as the law originally intended.
The AFL-CIO says benefits in many states are inadequate, and in 11 or 12 states the payment ''is only equal to . . . the minimum wage for a 40-hour week, '' even though most of the jobless are higher-paid industrial workers, according to Arleen Gilliam, an AFL-CIO social insurance specialist.
In Michigan, according to AFL-CIO figures, the maximum weekly benefit is $182 a week, while the average weekly wage is often from $200 to $300 a week.
* ''Traditional mechanisms that would have somewhat softened the impact of unemployment no longer exist or are severely restricted,'' says Ms. Gilliam - referring to recent cuts in food stamps, welfare, job training, public service employment, and other programs.
* Business also faces a loss of revenue as jobless benefits run out for idle workers, since unemployment compensation dollars ''turn over six or seven times'' in a community as they are spent and respent in business transactions, says Ms. Gilliam.
The AFL-CIO says it would be short-sighted for Congress and the administration not to pass an extension of unemployment benefits, but it is not optimistic about the prospects for the legislation now in Congress.
Democrats, the principal supporters of extended benefits, are nervous about being branded as big spenders at a time of pressure to hold down the federal budget.
On the other hand, conservative Republicans are just as wary about being tagged as heartless as hardships mount for the unemployed. Some say a good case can be made for extending benefits on a limited basis.
However, the administration has so far opposed extensions because of their potentially high cost. Its position is supported substantially by fiscal conservatives in both parties in the Senate.
Sen. Jeremiah A. Denton Jr. (R) of Alabama has sharply criticized jobless benefits for ''subsidizing unemployment.''
Pressures are also being applied in Congress by conservative business forces who contend that lengthening benefits will lessen incentives for the unemployed to take available lower-paying or less-skilled jobs.
Even if the 13-week extension is voted, it ''may be insufficient - it might not last long enough,'' Ms. Gilliam says.
''Most of the unemployed will not be able to qualify for food stamps or welfare because of new requirements on asset holdings and income,'' she says.
''They are going to lose their health insurance. Many are not going to be able to meet their mortgage payments or pay the bills most of us have. The question we must face is how we can help these victims of recession-bred record-high unemployment?''
So the AFL-CIO is also lobbying for the creation of job opportunities through employment incentive plans and aid to industries with high unemployment.