President Reagan supports the idea behind civil rights legislation that the Senate approved Thursday but would veto the measure because it "infringes upon state and local rights in many ways," presidential spokesman Marlin Fitzwater said yesterday.

The Civil Rights Restoration Act is designed to reverse the impact of a 1984 Supreme Court ruling that sharply restricted the government's power to withhold federal funds from educational institutions that discriminate. Under the court decree, the government may block federal aid to only the specific educational program or activity believed to be discriminatory, not to the entire institution.

The Senate measure, which proponents call one of the most sweeping civil rights bills to be approved in decades, would restore the power of the government to withhold all federal funds from many types of institutions, including governments, believed to discriminate against minorities, women, the elderly and the handicapped.

"What the bill does is dramatically to expand the federal jurisdiction over state and local governments, churches, synagogues, farms, grocery stores, including mom and pop stores, and businesses of all sizes," said Leslye Arsht, a Fitzwater deputy. She said the measure would force the government to suspend all payments to church-affiliated hospitals, for example, if a housing project run by the same church group was found to have inadvertently discriminated.

"It's a question of whether you discriminate against people who have no intention of discriminating," Arsht said. The administration, she said, supported a substitute offered by Sen. Orrin G. Hatch (R-Utah), which would have affected only educational institutions and would have allowed the government to block all funds from schools found to discriminate.

During Thursday's debate on the bill, opponents produced a letter from Reagan to Hatch calling the measure "unacceptable." But some senators questioned whether Reagan's threat is serious.

Fitzwater said yesterday that the veto threat is serious and that the president believes the bill, sent to the House on a 75-to-14 vote, goes too far in its effort overturn the 6-to-3 ruling in the Grove City College v. Bell.

"I would like to point out that the administration supported a bill that will overturn the Grove City decision and that we have said virtually from the time that the decision was made, that we opposed it . . . ," Fitzwater said, chiding the news media for failing to report the administration's position.

On another civil rights issue, Fitzwater said that Reagan had asked for a "full report" on a wide-scale FBI surveillance of groups and individuals opposed to the administration's Central American policies. "He is concerned because there should be no investigations of Americans for their political beliefs," Fitzwater said.

The president's call was echoed by Sens. David L. Boren (D-0kla.) and William S. Cohen (R-Maine), the chairman and the vice chairman of the Senate Select Committee on Intelligence. They sent a letter to Federal Bureau of Investigation Director William S. Sessions demanding a written report on the activities and expressing concern "about possible misuse of FBI resources. . . . "