The Secret Service should be given greater power to gather intelligence from other government agencies, and restrictions on FBI intelligence-gathering should be relaxed, according to a Treasury Department report on the shooting of President Reagan.

The report praises the performance of Secret Service agents during and after the March 30 assassination attempt outside the Washington Hilton Hotel, but makes 11 recommendations for tightening presidential security.

These include considering the revision of the Privacy Act and the Freedom of Information Act, which the report says have hampered the service in gathering intelligence.

Since the shooting Secret Service Director H. Stuart Knight has told House and Senate committees that domestic security guidelines issued in 1976 by then-attorney general Edward H. Levi have reduced information coming from the FBI by about 60 percent.

The report, prepared by general counsel Peter J. Wallison for Treasury Secretary Donald T. Regan, recommends that the guidelines be modified.

It says the Secret Service should be given an executive mandate to demand greater assistance from other federal agencies and that the administration should consider giving the FBI wider domestic intelligence-gathering powers by changing the Levi guidelines.

The report says the protective capability of the service has been impaired by "a critical overall decline" in the information it receives from the FBI, and that legislation on privacy and information access has made sources, such as in hospitals and police departments, reluctant to provide information they provided voluntarily in the past.

Yesterday Wallison said the decline in information "may have impaired the ability of the service to identify dangerous individuals and groups," and that this could jeopardize the president's safety, especially if a conspiracy were involved.

The report emphasizes the fortuitous circumstances of the March 30 attack: that it was made with a small-caliber handgun in daylight, that only an individual was involved and that it took place in Washington near a first-class hospital.

Wallison said the report was intended to deal with problems that could arise in more difficult circumstances, such as a a situation involving a conspiracy.

It recommends increased supervision of the service by high Treasury officials, improvements in data processing and tighter controls on information about presidential security and travel arrangements.

The report also calls for more agents and more money for the service; better liaison with White House advance teams on "protective procedures," which it says are now handled on an ad hoc basis; the addition of a paramedical team to the presidential entourage; the carrying of the president's medical records in his limousine; an automatic build-up of security around the president after a threat and better protection for the vice president and more secure communications on his plane.

At the time of the Reagan shooting Vice President Bush was in Texas, and the report notes that transmissions from his plane were in the clear and could have been monitored by anyone.

On liaison between the White House and the Secret Service, the report says that politics and security sometimes conflict, and that more agreement is needed between the White House and the Secret Service on guidelines.

Inside the Hilton elaborate security precautions were taken to protect the president from a pre-screened group, which was kept at a safe distance; outside, anybody could walk to a rope barricade only a few feet from him without any screening.

Despite the report's concerns about security it commends the agents in the Reagan protective detail on March 30. In particular, four agents were singled out: Jerry Parr, who pushed Reagan into his limousine upon hearing shots, Tim McCarthy, who was injured, D.V. McCarthy and Ray Shaddick. They are recommended for special awards.