The Republican Senate yesterday swept aside Reagan administration objections and voted to curb the power of federal regulators by giving Congress a veto over most of the rules proposed by government agencies.

By a 69-to-25 vote, the Senate overrode critics who questioned the constitutionality of a congressional veto and warned that it will unleash a new wave of special-interest lobbying by business and other organizations that dislike particular regulations.

The amendment was described by advocates as necessary to rein in independent agencies that exceed their authority and pass sweeping regulations never intended by Congress. "We've got to put restraints on the unbridled use of executive power," said Sen. Harrison H. Schmitt (R-N.M.), a principal sponsor. "We've got to be sure they don't overwhelm the legislative branch."

The amendment was added to a major regulatory reform bill that has wide support in the Senate. It will continue work on the complicated bill today. A House bill designed for the same purpose also contains a legislative veto, permitting only one house to disapprove a regulation but also permitting the other house to override that veto.

The amendment added by the Senate yesterday provides that both houses of Congress must pass a resolution disapproving a regulation in order to block it.

President Reagan has advised senators he is opposed to the legislative veto although he endorsed the concept during his presidential campaign.

If finally enacted and signed into law, it could have a sweeping effect on bureaucratic rule making and strengthen Congress in its battles with the executive branch. Nearly 200 separate pieces of legislation have been passed over the years containing congressional vetoes, but the amendment approved yesterday is the first to give that power over a broad range of federal regulations.

It would apply to most independent agencies and executive branch regulatory bodies. However, certain offices would be exempt, including all in the Department of Defense and most of the rule-making functions of the Internal Revenue Service. It would not apply to the Federal Reserve Board's monetary policy functions nor to the Securities and Exchange Commission's actions in corporate merger cases.

The congressional veto is under a big legal cloud as the result of recent U.S. appeals courts decisions holding the veto power unconstitutional as applied in two cases. Opponents yesterday seized on the constitutionality issue as a reason to avoid trying to draft a legally sound veto provision now.

"There could not conceivably be a worse time for Congress to put in place a government-wide veto," said Sen. John C. Danforth (R-Mo.).

Danforth also argued that it will subject members of Congress to additional lobbying pressures from interests that want an adverse regulation overruled. "This will magnify the role of the lobbyist," he warned.

But proponents argued that Congress must reclaim some of the power it has unwisely delegated to bureaucrats over the years. What Congress has done, said Sen. Carl Levin (D-Mich.), is "set loose on the American body politic a host of faceless decision-makers . . . who owe no allegiance to constituents" and whose concerns are "too often focused on their rules rather than the results.

"We created a class of people who were insulated from the political process and then we turned over to them the most important and sensitive of political issues involving the implementation of our laws."

A simple majority vote in both houses of Congress would be required to disapprove a specific regulation. The veto could apply only to proposed regulations not in effect when the bill becomes law.