J. P. Morgan & Co. Inc. yesterday reported net income rose 31.1 percent to a record $2.76 a share in the first quarter of 1983 from $2.09 a share in the previous first quarter despite a "significant" increase in loan loss provision.

Other banks and companies reporting improved first-quarter results yesterday included Irving Bank Corp., Marine Midland Banks Inc. and GAF Corp., while Celanese Corp. and Westinghouse said first-quarter earnings fell.

Morgan, whose principal subsidiary is the Morgan Guaranty Trust Co., the nation's fifth-largest bank, said net income rose 37 percent to $117.8 million from $86 million in the first three months of 1982.

Morgan attributed the rise principally to increased net interest income, but it said non-interest operating income more than doubled, chiefly because of sharply increased foreign exchange trading income and a reduction in net investment securities losses.

These gains were partly offset by provision for loan losses, which "increased significantly, reflecting management's concern about the financial condition of certain borrowers in the United States and abroad," Morgan said.

Morgan, along with other major banks, has adopted the controversial new Securities and Exchange Commission reporting rules that must be implemented by the end of 1983. These require reporting of net income instead of income before securities transactions that many analysts believe is a truer picture of a bank's operating health.

Irving Bank Corp., which also has adopted the new reporting rules, said earnings rose 15.5 percent to $24.06 million ($2.52 a share) from $20.84 million ($2.37) in 1982.

Irving, in contrast to most major banks, benefited from lower loan loss provisions in the quarter that was partly offset by a decline in net interest income.

Marine Midland Banks Inc., reported a 17.6 increase in first quarter earnings to $23.4 million from $19.9 million the previous year. Per share earnings rose 14.4 percent to $1.19 from $1.04 a year ago.

Edward W. Duffy, Marine Midland chairman, attributed the jump to increased net interest income and to "measures instituted to restrain non-interest expense growth while providing for investments in product development."

Caterpillar Tractor Co., the world's largest manufacturer of earthmoving and construction equipment, lost $172 million in the first quarter of 1983, company chairman Lee L. Morgan said.

The company had made a profit of $42 million in the first quarter last year, but lost $204 million in the fourth quarter of 1982. Sales fell nearly $1.2 billion to $796 million in the first quarter compared with the same period last year.

The company cited a seven-month strike by the United Auto Workers union, the recession and price competition for the earnings performance.

Morgan said Caterpillar's board of directors voted to continue to pay a reduced dividend of 37 1/2 cents per share.

GAF Corp. reported that profit rose 23 percent in the first quarter to $3.2 million (17 cents a share), from $2.6 million (13 cents) in the first three months of 1982.

GAF, a producer of building materials and chemicals, said earnings from continuing operations rose to $2.1 million in the first quarter compared with a loss of $3.8 million a year ago. Sales grew to $162.8 million from $139.5 million.

A major proxy fight by a dissident shareholder's group seeks to oust present management of GAF at the annual meeting April 28.