JACKSON, Miss. (AP) _ BellSouth Corp. dropped out of the bidding Monday for part of Jackson-based Mobile Communications Corp. of America and MCCA officials announced later that they were pulling out of a planned 17-story office tower in downtown Jackson.

''Extensive negotiations,'' based on the communications giant's ''firm proposal, had not resulted in a final agreement,'' Atlanta-based BellSouth said.

''BellSouth has enjoyed a close relationship with MCCA as its chosen joint venture partner for several years and regrets it has not been able to succesfully conclude the acquisition,'' the statement added.

MCCA officials announced last Monday that BellSouth had offered to buy MCCA's cellular telephone and local paging divisions and said last Thursday that other offers had been received.

BellSouth had proposed exchanging each share of MCCA Class A and Class B common stock for $24 of BellSouth common stock. MCCA officials have not identified other groups interested in purchasing the company, but MCCA Executive Vice President Rainer Sautermeister said during a news conference Monday that there were ''two or three.''

Sautermeister said any company ''has a right to make a bid, and we have an obligation ... to our stockholders to look at those proposals.''

If its cellular telephone and paging divisions are sold, MCCA would likely spin off its satellite paging, telephone anwering and marine telecommunications divisions into a separate firm.

Sautermeister announced during the news conference that MCCA's contract with Joseph C. Canizaro interests of New Orleans, developer of the MCCA Tower, had expired at 5 p.m. Saturday and the company would look for other office space.

MCCA is the nation's fourth largest radio common carrier with paging and cellular telephone interests in 100 cities in 30 states and the District of Columbia.

The company had revenues in 1986 of $70.8 million, up from $60.8 million in 1985.