American Telephone & Telegraph Co. said today the company would finance a shareholder lawsuit in an effort to prevent the Internal Revenue Service from taxing nearly $370 million in additional dividend income on AT&T shares held prior to divestiture.

AT&T Chairman Charles L. Brown also told a shareholder meeting that the company planned to cut its long-distance telephone rates on June 1 when it shifts onto local customers the $1-a-month access charge it now pays local telephone companies.

AT&T filed with the Federal Communications Commission today to lower long-distance rates for AT&T's long-distance, WATS and 800 services by 5.6 percent and to reduce rates to 87 countries by up to 6.6 percent. Brown said the rate cuts, which had been expected, would save long-distance telephone users $1 billion a year.

Brown also used the stockholder meeting to announce a 34 percent increase in first-quarter earnings over the comparable period a year ago. He said earnings for the three months ended March 31 were $354 million (31 cents per share) compared with $226 million (20 cents) in the first quarter of 1984. AT&T revenue for the first three months was $8.3 billion compared with $8.14 billion for the first quarter of 1984.

The pending legal fight with the IRS involves the agency's previously announced plan to raise the amount of taxable dividend income by 39 cents a share on old AT&T stock distributed prior to the breakup of the Bell System Jan. 1, 1984.

"We are going to actively support a shareowner's court challenge to the IRS position," Brown said to the applause of nearly 2,000 shareholders. "AT&T will pay the costs of litigation."

The lawsuit cannot be filed by AT&T but must be filed by shareholders, an AT&T spokesman said. One AT&T institutional shareholder will file the suit, but AT&T declined to specify which institution would file and when. "The details are still being worked out," the spokesman said. Should the one investor win the suit, all shareholders would receive a refund, the spokesman added.

The IRS has decided to raise its estimate of taxable dividend income because of outstanding shares AT&T acquired in the regional telephone company Pacific Telesis after the announcement of the Bell System breakup in January 1983, according to an AT&T spokesman.

"Before divestiture, we owned 90 percent of Pacific Telesis stock and took steps to acquire all of Pacific," said spokesman Dick Gray. "We announced divestiture in January 1982, completed the acquisition in May 1982, so the IRS considers that is taxable as a dividend to the shareholders."

AT&T maintains that the shares should not be taxed because the assets were not acquired as part of an overall divestiture strategy to increase dividends. AT&T had appealed to the IRS and Congress to no avail, he said.

Shareholders with AT&T stock as of Dec. 31, 1983, must declare 39 cents per share in additional dividend income on their 1984 taxes, said an IRS spokesman. "We definitely feel it is taxable," he said.

As of Dec. 31, 1983, there were about 966 million shares outstanding, said an AT&T spokesman, who estimated that about $370 million would be taxable. It is not clear how much the IRS would actually receive because of varying shareholder tax brackets and tax exemptions.

Brown told the shareholders that the earnings results released today showed "no surprises." The improvement in AT&T earnings reflects continuing transformation of the company from a monopoly to a competitive company, he said.

Overall, AT&T earned $1.38 billion in 1984, trailing its own forecasts and analysts' estimates. Right before the breakup, the company had predicted a profit of $2.1 billion ($2.02) for 1984. Actual profit equaled $1.25 per share on revenue of $33.2 billion. For the fourth quarter, the company's profit was $379 million (34 cents) on revenue of $8.41 billion.

But AT&T's long-distance business is going strong this year, bolstering the financial picture, said analyst Harry Edelson of Edelson Technology Partners in Saddlebrook, N.J. Long-distance sales have been the company's ace, generating 60 percent of AT&T's $147 million in net income last year, he said.