President Carter got out front yesterday in the defense budget battle by telling congressional leaders he could not support increases in spending beyond 3 percent annually over the next three years.

Sen. Ernest F. Hollings (D-S.C.) told The Washington Post that, after receiving word yesterday morning of the administration's position from Defense Secretary Harold Brown, he and his Senate allies decided to keep fighting for 5 percent increases beyond fiscal 1980.

"Brown said they'd go for three, three and three," Hollings said of percentage increases for fiscal 1980, 1981 and 1982, "but we're going to go for three, five and five."

Also, Hollings added, he and other senators have asked to meet with the president to make their case for 5 percent increases for fiscal 1981 and 1982. Hollings said White House officials told him such a meeting might be possible today.

Hollings, Sens. Sam Nunn (D-Ga.), Henry M. Jackson (D-Wash.) and John Tower (R-Texas) lead the Senate drive to raise congressionaly-imposed money ceilings to accommodate increased military spending.

They will make that effort on the Senate floor, probably tomorrow, by moving to raise the previously established budget ceilings.

Nunn, Jackson and Tower have told Carter that annual increases of 4 to 5 percent in military spending, after allowing for inflation, are necessary to make the pending strategic arms limitation treaty an acceptable risk.

Some members of the administration fear that by failing to go along with such increases, the White House jeopardizes ratification of the SALT II treaty, even though the president himself opposes linking the two.

Rather than come out flatly against 5 percent increases in fiscal 1981 and 1982, some administration officials argued yesterday as the president's letter to Hollings and others was being drafted that it would be better to remain vague about future military spending.

"Maybe that's why I haven't gotten the letter yet," said Hollings last night. "I'd jump off the Washington Monument if he ends up saying in the letter he'll go along with 5 percent."

Besides the linkage to SALT II, the Senate effort to raise budget ceilings has been boosted by recent disclosures of the Soviet combat brigade in Cuba.

Hollings intends to attack the contention that extra billions for the Pentagon would amount to financial over-kill -- an argument that prevailed Monday in the House when it refused to raise government budget ceilings to allow for big hikes for defense.

Assuming a 7.8 percent rate of infaltion, here is how much money Senate staffers figure would be required under the rival proposals for financing national defense: