NEW YORK, JULY 16 -- American Telephone & Telegraph Co.'s stock rose to its highest point since the 1984 breakup of the Bell System today as the company announced a 41.2 percent increase in its second-quarter profit.

One of AT&T's offspring, New York-based Nynex Corp., said its profit rose 3.9 percent in the second quarter.

AT&T warned that its increase was boosted by one-time factors, but investors nevertheless took heart that the world's largest telecommunications company was bringing its costs under control.

"The moon and the stars seem to have aligned properly in the second quarter," Robert Kavner, AT&T's chief financial officer, told a crowded meeting of financial analysts. But he added, "They {results} are not an excuse for us to relax. We've got a lot to do."

AT&T stock rose $1.50 a share, to $31.75, in consolidated New York Stock Exchange trading.

AT&T said it earned $596 million (55 cents a share), up from $422 million (37 cents) a year earlier. Revenue slipped a fraction of 1 percent, to $8.4 billion from $8.42 billion.

For the first six months of 1987, AT&T said its profit rose 35.9 percent, to $1.04 billion (95 cents) from $776 million (68 cents). Revenue fell 3.6 percent, to $16.52 billion from $17.13 billion a year earlier.

Several factors inflated the year-to-year comparisons.

Unusually high settlements of discrepancies in access charges added $50 million to profits in the second quarter, Kavner said. Moreover, the year-earlier quarter included a 26-day strike that cost about $140 million, and the first half of 1986 included a charge of $175 million for a change in accounting for depreciation.

AT&T has cut tens of thousands of workers from its payroll and closed offices and factories in an effort to streamline its operations since it was broken up under an antitrust consent decree with the Justice Department in 1984.

Although it continues to dominate long-distance communications, it has had unsatisfying results in sales of computers and equipment.

"These results show that our long-distance business remains strong and reflect the early-stage benefits of ongoing cost-reduction efforts as well as productivity and efficiency improvements," AT&T Chairman James Olson said in a statement. Olson warned that AT&T could not guarantee that its profit in the second half would be as large as in the first half, but said, "We expect to continue doing better than we anticipated when the year began."

Kavner responded to a question about whether AT&T could manage to earn $2 a share for all of 1987 by saying it would be a long stretch. But he added, "We'll do our best."

AT&T is ideally situated to take advantage of the growing importance of communications to the business world, said Charles Nichols, an analyst for E.F. Hutton & Co.

But one skeptic, Donald Haback of Nikko Securities International Co., said AT&T has not shown an ability to reach out past its traditional customers in the equipment business. Nynex, the Bell telephone holding company serving New York and New England, said its second-quarter profit rose 3.9 percent, to $322.8 million ($1.58 a share), from $310.8 million ($1.54) a year earlier. Revenue rose 6 percent, to $3.01 billion from $2.84 billion. For its first half, Nynex said its profit rose 2.4 percent, to $621.9 million ($3.05) from $607.3 million ($3) a year earlier. Revenue rose 7.1 percent, to $5.90 billion from $5.51 billion.