President Reagan had what doctors called his best day since he was shot here March 30, and presidential press secretary James S. Brady spoke twice on the telephone yesterday as he continued his remarkable recovery from a bullet in the brain.

Brady, who doctors thought had a 90 percent chance of dying when they first saw him after the shooting outside the Washington Hilton Hotel, was reported likely to recover most of his mental capability.

Dr. Dennis O'Leary of George Washington University Hospital was described by deputy White House press secretary Larry Speakes as being "extremely optimistic" that Brady will be able to resume his White House duties eventually.

"We're reasonably confident that Brady is going to have a pretty full recovery of his mental function," O'Leary said.

Brady's temperature is normal and he was taken off antibiotics yesterday. "Some of these patients will wax and wane a little bit -- and he may yet," O'Leary said yesterday, but he called Brady's rate of recovery "a good bit faster than average."

Brady spoke to his deputy, Speakes, and to Vice President Bush's press secretary, Peter Teeley, in separate phone calls from his hospital room.

"For all of us here in the White House, this is nothing short of a miracle," Speakes said later.

The conversations were only a few minutes long, but Speakes and Teeley said Brady's voice was strong and clear. Teeley and Brady picked up a running joke between them about fishing for sharks. "Hey, we're still on for that fishing trip this summer," Teeley told Brady. Teeley has been proposing fishing for sharks with rods and reels, and Brady, facetiously, has counterproposed using dynamite. Brady was adamant yesterday. "No, we need the dynamite. It wouldn't be any fun without it," Teeley remembered Brady saying.

Speakes said his conversation with Brady centered on the running of the White House press office and said he assured Brady that everything was fine. w

O'Leary said that he and Dr. Arthur Kobrine, the surgeon who operated on Brady, would not be surprised to see his emotional reactions " a little flat because the injury bears some resemblance to a frontal lobotomy. But he is not behaving like a lobotomy patient." Kobrine estimates that less than 20 percent of the tissue of the right half of Brady's brain was removed, and not all of it was from the frontal lobe.

O'Leary said Brady has shown some anger, humor and depression, and "all of us feel that's a good sign."

Reagan was reported to have had a normal temperature for more than 24 hours and doctors continued to speak of his returning to the White House this weekend, with Saturday the most likely day. White House physician Dr. Daniel Ruge said that "this is the president's best day yet."

Reagan, who works between 1 1/2 and two hours each day, according to aides, issued a statement yesterday mourning the death Wednesday night of General of the Army Omar N. Bradley.

"Even as he rose in rank, humility never left his side," Reagan said of Bradley. "He was the 'GI's general' because he was, always, a GI."

The president added that he and Nancy Reagan were honored to have had Bradley as their friend and by Bradley's appearance at the president's inauguration in January.

Reagan also issued a statement hailing the NATO defense minister's formal linkage of arms control negotiations to Soviet international behavior. He called the move "a signficant contribution to prospects for world peace."

He also received visits from Senate Minority Leader Robert C. Byrd (D-W.Va.) and House Minority Leader Robert H. Michel (R-Ill.), whom he gave a letter deploring the House Budget Committee's obstructions to implementation of his economic recovery package.

In another development, the FBI has been trying to find the shirt, tie and a cufflink Reagan was wearing when he was rushed to the emergency room March 30. They were lost in the confusion of aiding the wounded president, Brady and Secret Service agent Timothy J. McCarthy.