Alexandria's new mayor, Charles E. Beatley Jr., angered by the criticisms of a private cable television firm, has ordered city officials to try to strengthen controls over the recently franchised company.

Beatley, who took office July 2, three days after Alexandra's lame duck City Council voted the company an exclusive cable franchise, also said yesterday he will take a direct hand in upcoming contract talks with the firm.

Beatley said he was irked by the tone of a recent letter critical of the city's franchise-granting procedures from executives of the winning bidder, Alexandria Cablevision Co. (ACC).

"They have made a lot of promises, and those promises ought to be formalized. I have a gut feeling that things aren't finished yet," Beatley said.

Beatley's statements were his first public comment on the hotly contested franchise, which Alexandria Cablevision Co. won over two competitors.

The firm's letter and Beatley's response come on the eve of discussions between the two sides on a performance contract scheduled to be signed July 26, to spell out blinding terms for the potentially lucrative cable system.

Beatley said yesterday he had instructed the city staff to investigate whether "buy-out" . . . clause would allow the city to purchase the system if it was dissatisfied with the company's performance.

Beatley was furious last week when Alexandria Cablevision delivered its letter, sharply criticizing the city procedures used in awarding it the potentially lucrative contract.

"That letter raised more questions about ACC than it raised about the city manager or his staff," Beatley said, declining to state what the questions were. He said that the effect of the letter was to force him to change his own plans and get directly involved in the contract discussions, rather than leaving the matter to his staff.

"I hope ACC would be able to continue as the franchise winner . . . but the citizens have a right to be protected," he said.

Charles Henry Smith Jr., chairman of the Cablevision firm, said yesterday that "not having been a part of the negotiations up to now, he [Beatley] cannot understand our concern" at alleged improprieties by the city staff.

The outgoing City Council, chaired by then-mayor Frank E. Mann, awarded Alexandria Cablevision the 15-year franchise one day before its term of office expired. On July 2, after Beatley and the new council had been sworn in, the firm delivered its letter, addressed to "Mayor Mann" and the council, attacking the city's procedures as (seriously flawed."

Beatley yesterday defended city financial consultant Lee A. Bertman and cable administrator Mary Sue Smoller, who were singled out for criticism by Alexandria Cablevision. Beatley said he had found no problem with their work.

"If you can have substantial differences of opinion on procedures before signing [the contract,"] Beatley said, "then you can have even greater differences afterward when it's easier to have them."