MCI Communications Corp. yesterday announced an agreement to sell all of its paging and cellular radio operations to Mobile Communications Corp. of America, then within two hours backed out of the deal when it discovered a regional telephone company was to acquire an interest in the operations.

MCI officials said they knew when they signed a letter of intent that BellSouth Corp. of Atlanta was somehow involved in the transaction, but did not know until they read a press release that the phone company was to acquire any of MCI's businesses.

MCI said it objected to BellSouth's role because "Bell companies ought not to be involved in local exchange services outside of their regional territory," said MCI spokesman Gary Tobin.

"BellSouth's involvement makes it highly unlikely the MCI board will approve the deal," said Tobin. MCI could agree to the deal if it were "not contingent upon any Bell operating company's involvement," he said.

"The Bell operating companies are devoting a major part of their resources and time to getting into other businesses," Tobin said, and as a result are delaying investments in facilities that would make it easier for customers to use companies besides American Telephone & Telegraph Co. for long-distance service.

Under the terms of the Bell System breakup in January 1984, regional telephone companies were supposed to give all long-distance companies the same kind of service provided to AT&T, eliminating the need for customers to dial lengthy codes to reach AT&T's competitiors. MCI recently complained to the Justice Department that the phone companies are dragging their feet.

Tobin said MCI wanted to sell its cellular and paging businesses because they don't "fit into our strategy, which is to provide national and international long-distance services."

MCI holds an interest in 12 cellular systems and provides paging services in six cities, including Washington, D.C., through MCI AirSignal. Cellular mobile phone systems use computer-controlled networks of radio transmitters to route telephone calls to mobile phones.

MCI and MCCA of Jackson, Miss., had signed a letter of intent in which MCI would sell the facilities for $121.5 million to MCCA's American Cellular Communications Corp.

In its press release announcing the deal, MCCA said it had completed a preliminary agreement with BellSouth to form a new joint venture to provide cellular phone service. As part of the agreement, BellSouth is to buy 3 million shares of MCCA common stock for $36 million and invest an additional $60 million in the joint venture.

MCCA issued a statement saying it still hopes to complete the transaction despite MCI's objections.

The Justice Department is investigating whether phone companies should be allowed to operate cellular systems outside their local area. It also is studying whether to permit a phone company to invest in cellular networks owned by companies not in the phone business.

The Federal Communications Commission is awarding two cellular licenses in each city, giving one automatically to the local phone company and setting aside the other for the phone company's competitors. The Justice Department contends that under terms of the Bell breakup, phone companies need special permission to buy into the "non-phone" cellular systems. Pacific Telesis, the California regional Bell company, says it plans to purchase a cellular commpany, Communications Industries Inc.