The U.S. Postal Service board of governors yesterday agreed to the concept of an electronic mail system which would allow the postal service to compete in the electronic transmission of messages with private firms. But the plan was rejected and sent back to the Postal Rate Commission for consideration of several "technical" points.

In its unanimous decision, the governors said they agreed with the basic premise of the rate commission's controversial decision, "that of full and free competition for the electronic transmission portions of the system with access to the postal delivery network available to all on a nondiscriminatory basis."

But the governors also said that the postal service "on the basis of demonstrated need" should be allowed to have its own telecommunications transmission system in competition with private firms.

The electronic mail plan would allow mailers, usually private companies, to transmit computerized messages to post offices, which would print the messages, place them in envelopes and deliver them within two days anywhere in the country. The service would be used primarily for heavy mail users whose mail is based on computerized lists such as customers' bills.

The governors yesterday requested several revisions in the rate commission's decision.

They recommended that the rate commission specify the postal service's authority to accept the electronic messages and permit the postal service to require assurances of performance from the telecommunications common carriers that participate in the system.