Governors of the U.S. Postal Services unanimously approved yesterday proposed increase in postage rates, including for the first time a two-tier first-class rate structure of 13 cents an ounce for individuals and 16 cents for businesses.

Postmaster General Benjamin F. Bailar told his board the increase are needed to offset an expected $2.4 billion deficit in the 12 months beginning next March 25, losses anticipated from increases in labor, fuel and other costs.

A formal petition seeking the higher rates is expected to be filed later this month with the independent Postal Rate Commission, which has 10 months to hold hearings on the plan and reach a decision. Thus, the higher rates being suggested are not expected to take effect until mid-May 1978, at the earliest.

In hearings before the commission, many business organizations are expected to oppose Postal Service's new "citizen rate" for individual consumer letters of 13 cents, unchanged from the current rate.

The U.S. Chamber of Commerce has denounced the concept and stated that increased postage costs for busines will be passed along to consumers in any event.

Although there never have been two different first-class mail rates, Bailar said yesterday he not only expects the concept to work, "but I'm going to accept the responsibility to make it work." The special "citizen rate" was suggested to the Postal Service by President Carter.

The new "citizen rate" will require use of a special stamp, standard-sized envelopes and the ZIP codes of both the sender and the addressee. Moreover, one of the addresses on such letters must be handwritten. If the new rates are approved, Bailar said an appropriate procedure will be announced under which consumers may continue to use existing 13-cent stamps until they are exhausted.

In terms of priority treatment at post office, 16-cent mail will be sorted first and the citizen's letters later but Bailar said emphatically that "for all practical purposes" there would be little difference in delivery standards.

Rate increases proposed by the board yesterday are designed to help the Postal Service break even, officials said. At the same time, they said postal volume likely will be affected.