WASHINGTON - With the jobless rate rising even as the recession eases its grip, the U.S. House of Representatives is expected to pass a bill this week to extend unemployment benefits for those who risk exhausting them.

The House is scheduled to vote on Tuesday on the measure to extend jobless benefits for another 13 weeks in hard-hit states, according to a schedule released by House Majority Leader Steny Hoyer.

Hoyer, a Democrat, scheduled the vote under special rules reserved for noncontroversial bills, a sign that it is expected to pass easily.

Senate leaders have said they expect to extend unemployment benefits as well, but it was not immediately clear when that chamber would act.

The unemployment rate rose to 9.7 percent in August, the highest figure since 1983, and is expected to remain high into next year even as the economy recovers from the worst economic downturn since the Great Depression of the 1930s.

Roughly 6 million people were collecting long-term unemployment benefits at the end of August, and some 1.5 million could exhaust those benefits by the end of the year.

Congress has already extended benefits for up to 79 weeks from the usual 26 weeks. Because the program is administered by the states, payments and the length of time people are eligible for benefits can vary.

The House bill, sponsored by Democratic Representative Jim McDermott, would cover roughly 300,000 workers whose benefits are projected to expire by the end of September. It would apply to workers in the 29 states where the unemployment rate is above 8.5 percent.

(Reporting by Andy Sullivan; editing by David Alexander)