WASHINGTON — The cash-strapped U.S. Postal Service is raising rates for its more profitable express mail and priority mail shipping next year, part of its efforts to stave off bankruptcy.

The new prices, which take effect Jan. 22, include the introduction of a new flat rate of $39.95 for overnight express mail boxes weighing up to 70 pounds that are sent domestically; the flat rate for express letters is being increased separately to $18.95. Previously, prices for the overnight service were $13.25 or higher based on package weight and distance.

The prices for priority mail, which promises two-to-three-day delivery, also will increase by an average of 3.1 percent.

The post office said the rate hikes were partly aimed at keeping the ailing agency afloat while maintaining its pricing advantage in the shipping business. Private companies such as UPS and FedEx, which offer similar express shipping services, regularly adjust their prices and have posted modest profits in the sluggish economy.

In the past year, the post office lost $5.1 billion, mostly due to a 5.8 percent decline in revenue for first-class mail. Priority mail and express mail posted a 6.3 percent increase.

Still, the new rate increase will make only a small dent in the Postal Service’s losses, caused by the recession, movement of mail to the Internet and a requirement that the agency fund future retiree medical benefits years in advance.

Among the priority mail rate increases set for Jan. 22: small box, $5.35; medium box, $11.35; large box, $15.45; regular envelope, $5.15; and legal-size and padded envelope, $5.30.

The new prices amount to an across-the-board increase of roughly 5 percent in postal shipping services. They are in addition to a previously announced 1-cent increase in first-class mail to 45 cents, also planned for Jan. 22. The independent Postal Regulatory Commission will review the proposed increases before they take effect.

Postmaster General Patrick Donahoe has warned that the post office could face bankruptcy next September unless Congress acts quickly to give the agency greater flexibility to close underperforming offices, reduce delivery to five days a week, raise stamp prices and reduce health care and other labor costs. The Postal Service, an independent agency of government, does not receive tax money for its operations.