Financially ailing Braniff International announced yesterday that it has reached agreement with its major lenders to extend payment on its debt and interest until next year.

Under terms of the agreement, Braniff's 39 lenders -- banks and insurance companies -- deferred until Feb. 1 all principal and interest payments on the Dallas-based airline's massive debt, estimated at almost $600 million. During that time, no additional interest will accrue on the debts.

Braniff also agreed to enter "intensive negotiations" toward reaching an agreement in principle by early fall on restructuring its debts. The final documentation of the restructuring is to be completed as soon as possible but no later than Feb. 1, Braniff said.

"We are pleased with the agreement," Braniff Chairman John J. Casey said yesterday. "It constitutes an expression of confidence in Braniff and its employes as well as in the soundness of its operations.

"We are optimistic that an acceptable restructuring agreement will be negotiated in the near future," he added.

Braniff's agreement with its lenders came at the last possible moment. Earlier this year, to help out the airline, which was virtually out of cash, Braniff's lenders had agreed to let it defer until July 1 about $40 million in principal and interest payments that were due between March 2 and June 30. It could not have made those payments.

Braniff said that as of Dec. 31 its long-term debt totaled $583.6 million. The company had estimated that interest payments alone on that debt would total $91 million this year.

Braniff reported a consolidated loss of $131.4 million in 1980 after a loss of $44.3 million the year before. During the first quarter of this year, Braniff reported an operating profit of $454,000 compared with a $22.5 million operating a year earlier. But non-operating expenses -- primarily the overwhelming interest on its debt -- brought the net figure for the quarter to a loss of $24.7 million.

The airline's financial woes stem generally from an aggressive and expensive route expansion program following passage of the airline deregulation law, just about the time the economy turned sour and fuel prices soared.

As part of its plan to get back into financial shape, Braniff laid off some employes, got the others to accept a 10 percent pay cut and cut back its operations by almost one-third.

In another airline industry development, Boeing Co. said it had sold to Air Florida five 727 jet aircraft originally ordered by Braniff. Three 747s ordered by Braniff haven't found buyers yet.