Braniff International is seeking a new agreement with its major lenders to extend payment on its debt and interest beyond the current July 1 grace period, John J. Casey, chairman of the financially ailing airline, told shareholders today.

To help out the airline, which was virtually out of cash, Braniff's 39 lenders earlier this year agreed to let Braniff defer until July 1 about $40 million of principal and interest payments that were due between March 2 and June 30.

Casey said Braniff was working on restructuring its massive debt -- principal and interest payments will total about $181 million this year -- and hopes to work out a deferral schedule in meetings with lenders scheduled during June. "There is nothing firm on this," he said.

Today's meeting, held at the company's headquarters on the airport grounds, was a mixture of hard realism and cautious optimism. In a departure from typical shareholders meeting bravado, Casey started out immediately with a report on the finances of the company in which he minced no words about its precarious straits. Its debt burden as it began 1981 totaled about $673 million consolidated loss last year.

Casey also cited the same list of problems that hit other airlines lasy year, including new competition, increases in fuel prices and other costs, and recession-prompted declines in passenger traffic.

"As if those weren't enough, we contributed one more problem of our own -- poor judgement, particularly as it related to overzealous expenditures for expansion," he said, referring to Braniff's aggressive out expansion following passage of the airline deregulation law. "These problems and resulting losses have had devastating and convulsive effects upon Braniff's financial posture," he said.

But Casey, who was elected chairman after Harding L. Lawrence resigned as chairman and chief executive officer at the end of 1980, contended the airline's new operating plan already has begun to pay off. It involved the layoff of some employes, an across-the-board 10 percent pay cut for employes and a 30 percent cutback in Braniff's operations. In addition, Casey waived his salary.

"We've turned the corner from an operating downslide," Casey said, noting that the airline reported a slight operating profit of $454,000 in the first quarter, compared with a loss of $22.5 million for the first quarter of 1980. However, nonoperating expenses, primarily the overwhelming interest on debt, brought the net figure for the quarter to a loss of $24.7 million, he added.