President Reagan is exercising regularly in his hospital suite and is making such a rapid recovery that he is likely to be able to leave the hospital for the White House next week, Dr. Dennis O'Leary, a spokesman for George Washington University Hospital, said yesterday.

"His progress is super," O'Leary added.

Reagan was visited by Vice President Bush, senior White House aides and Sens. Howard H. Baker Jr. (R-Tenn.) and Paul Laxalt (R-Nev.). "I found out it hurts to get shot," the president told the senators.

Despite post-operative pain, Reagan is taking only mild pain medication, "about what you take for a headache," O'Leary told reporters at the White House.

White House press secretary James S. Brady, the most seriously wounded of the four men shot outside the Washington Hilton Hotel on Monday, continued to improve and yesterday held "a restricted conversation" with his doctor.

When asked how he was feeling, Brady replied with a thumbs-up sign and said, "Fine, fine." Brady is also performing breathing exercises on instructions and has gained minimal voluntary movement of muscles in his left arm and leg, doctors said. He remains, however, in critical condition.

O'Leary said that a doctor asked Brady how many fingers he was holding up and Brady correctly replied "three." A reasonably good assessment of Brady's brain damage will have to wait for a couple of weeks and a more-or-less final assessment won't be possible for six to 12 months, O'Leary said.

A federal judge ordered the man accused of shooting Reagan, John W. Hinckley Jr., to undergo further mental tests although one court-appointed psychiatrist said Hinckley is fit to stand trial.

Hinckley wore a bulletproof vest to his brief court appearance.

The president was not wearing a bulletproof vest because the Secret Service had no intelligence information to lead them to believe he faced special danger Monday, Secret Service officials told a Senate subcommittee. Reagan has said he will wear a bulletproof vest anytime security officials ask him to.

Hinckley was not known to the Secret Service, but another man who is considered a potential assassin was waiting outside the hotel Monday, Secret Service Director H. Stuart Knight testified.

This was the man witnesses described as having been acting strangely before Reagan emerged from the hotel. An agent spotted this man and took unspecified steps to insure that he could not harm the president, Knight said.

The subcommittee also was told that if the Secret Service had been informed of Hinckley's arrest in Nashville with handguns in his luggage about the time President Carter visited the city, Hinckley would have been interviewed by the Secret Service and might have been placed under regular observation.

At the White House, Bush went through a crowded day made up partly of events that had been scheduled for the president and partly of meetings on his own schedule.

Against the background of new concern about events in Poland, Bush met with Polish Deputy Prime Minister Mieczyslaw Jagielski in the Roosevelt Room and then publicly announced that the United States will provide Poland with $73 million worth of surplus dried milk and butter at concessionary prices. Poland will pay only $50 million and, in the major concession, the United States will accept payment in Polish zlotys. Poland has no hard-currency reserves.

Bush read a statement for reporters reaffirming U.S. support for a solution of Poland's problems through peaceful negotiations and warning against a Soviet invasion of Poland.

The vice president also chaired a Cabinet meeting and received two groups of Republican members of Congress.

By a string of small changes from the way such White House events would have been arranged for the president, presidential aides and Bush are sending out symbols to reinforce their main point -- that Bush is acting for the president, but does not have presidential powers.

Bush is holding many of his meetings in his own White House west wing office and others in the Roosevelt Room. He has not used the president's Oval Office.

Instead of appearing with the Polish minister on the south side of the White House where such ceremonial events usually take place, the two men and their aides posed in front of the west wing. One purpose of the change was to make sure the photographs would not have the White House background traditional in so many thousands of pictures of the president.

Bush met the Republican members of the House Ways and Means Committee and the House Budget Committee and a group of about 40 labor leaders as part of the continuing administration effort to sell Reagan's program of federal spending cuts and tax reductions.

The president made a similar pitch to labor union leaders at the Washington Hilton Hotel just before he was shot.

The leaders of the AFL-CIO and other unions have attacked Reagan's spending cuts as unfair to the poor and unemployed.

For the second day in a row, White House officials refused reporters' requests for a photograph of the president as he recuperates in the hospital. Senior presidential advisers have decided against having the president's picture taken until he had had more time to heal, and Dr. O'Leary said yesterday that he agreed with the decision.

"Well, I think it's a combination of respecting his privacy. It's a medical preference not to [have his picture taken] and I think it is the White House's preference. He looks fine," O'Leary said.

O'Leary said Reagan had a good appetite and his cheeks are rosy. He "wolfed down" orange juice, honeydew melon, two soft-boiled eggs, whole wheat toast with honey and decaffeinated coffee for breakfast, O'Leary said. For lunch, Reagan ate chicken broth, carrot sticks, celery and radishes, crackers, banana ice cream, cookies and water.

He watched some of the morning television news shows, read newspapers and the White House news summary and, keeping his ideology in trim, read some of the National Review, according to a statement issued by the White House press office.