International Business Machines Corp. said yesterday that its first-quarter profit climbed 24 percent from a year earlier on a 17 percent revenue gain.

IBM, the world's largest computer maker, attributed the higher results in part to increased customer purchases of new products and installed equipment that was previously leased.

And in other major quarterly reports issued yesterday:

* Chemical New York Corp., the nation's sixth-largest bank holding company, reported a 16 percent gain in first-quarter earnings.

* American Express Co., the diversified financial and travel services organization, said all four of its divisions showed strong showings.

* W. R. Grace & Co., the international chemical and natural-resources concern, said its first-quarter profit plunged 77 percent from a year earlier.

IBM's profit rose to $976 million ($1.62 a share), from $789 million ($1.33) in the first quarter of 1982. Revenue increased to $8.29 billion from $7.07 billion.

The results were "right in line" with analysts' expectations, said John J. McManus of Bear, Stearns & Co.

IBM said its after-tax profit margin--which is net income expressed as a percentage of total revenue--climbed to 11.8 percent from 11.2 percent a year earlier.

IBM Chairman John R. Opel said that the company's new products--including new models of its personal computer, System 38 family of medium-size computers and Series 1 group of general-purpose minicomputers--"should continue to have a positive effect on new order activity in 1983."

Shipments of IBM's large-scale mainframe computers, and of its 3380 data storage devices "continue to be very strong," Opel said.

IBM said its first-quarter revenue from equipment sales rose 44.5 percent to $3.97 billion from $2.75 billion, while rental revenue fell 9.4 percent to $2.58 billion from $2.85 billion.

Chemical New York Corp., the nation's sixth-largest bank holding company, which operates Chemical Bank, the six-largest commercial bank, said first quarter net was $71.5 million, up from $61.7 million. Per share results, reflecting issuance of additional stock, were $2.45, up from $2.41.

Chemical said net interest income was $385.7 million, up 14 percent from $337.4 million in 1982.

Chemical said its loan loss provision, funds set aside for protection against possible defaults, was $28.7 million, up from $15.6 million. Actual charge-offs of bad loans almost tripled: $28.5 million, compared with $11.4 million.

American Express Co., reported first quarter earnings were $162 million, up 37 percent from $118 million a year ago.

Revenue rose to $2.3 billion from $1.8 billion, a 27 percent increase. Earnings per share were $1.20, up from 93 cents.