The post office expects to lose $6 billion this year and is seeking help from Congress to fix its finances.
Barnett said the increases, if approved, would generate $2 billion annually for his agency. The agency last raised postage rates on Jan. 27, including a penny increase in the cost of first-class mail to 46 cents.
The Postal Service unsuccessfully sought an emergency 5.6 percent rate increase in 2010, citing the recession.
The commission acknowledged that the recession had hurt revenues, but said the rate request was more of an attempt to address long-term structural problems.