The Reagan administration moved to reassure Americans about its forthcoming budget cuts with word yesterday that seven programs -- including Social Security's basic retirement benefit, Medicare and veterans' benefits -- are safe from the ax of Office of Management and Budget Director David A. Stockman.

White House press secretary James S. Brady said Stockman told a Cabinet meeting about the seven safe programs at the time he reported that his group looking for places to trim the federal budget has identified more than 90 percent of the reductions that will be recommended to President Reagan. The president is to make the list public Feb. 18.

Treasury Secretary Donald T. Regan, who briefed the Cabinet on tax policy yesterday, confirmed that the administration is considering proposing two tax bills in an effort to keep the first one limited to the 10 percent tax cut in each of the next three years plus increased depreciation allowances for business. The second bill will be used to introduce other measures.

However, Senate Finance Committee Chairman Bob Dole (R-Kan.) said that members of Congress want to wait for a second bill [Details, Page E1].

As a way of pinning Congress down on spending, the administration is considering asking it to commit itself immediately to a dollar figure by which it will cut the budget, and to work out later which programs will be cut, The Chicago Sun-Times reported.

The seven programs Stockman identified as safe will be funded as proposed in former president Carter's 1982 budget, Brady said. Their total cost is about $210 billion.

The most expensive of the protected programs are politically popular supports for millions of Americans across the economic spectrum, not programs targeted to aid the poor.

Even with the political tide running strongly in favor of slashing the federal budget, Social Security, Medicare and veterans' benefits have strong backing and were not considered targets for big cuts.

The seven:

The $140 billion basic retirement program of Social Security that benefits 32 million retirees, dependents and survivors.

The $45.4 billion Medicare program, which serves 28.6 million people.

Supplemental Security Income, which provides $7.9 billion, mostly for the blind, disabled or elderly poor. It has about 4.2 beneficiaries.

Benefits for 2.3 million veterans with service-related disabilities, at a cost of $8.6 billion, and for 1.8 million pensioners with non-service-related disabilities, costing $4.1 billion.

The core of the free school lunch and breakfast programs, which provide meals for 9.5 million needy youths at a cost of $2.1 billion.

Operation Head Start, which aids poor, mostly inner-city, pre-school children. It costs $950 million and reaches 374,000 children.

Summer jobs for youths, which employ 665,000 people at a cost of $870 million.

Brady said the preservation of these programs is in keeping with Reagan's pledge not to deprive the "truly needy" have been defined as those who probably could not survive in the absence of government benefits, said Donald W. Moran, associate director of OMB for human resources, veterans and labor.

Two of the protected services that are targeted most directly on the needy -- Operation Head Start and the summer jobs program -- are considered good investments, Brady told reporters.

He quoted Education Secretary Terrell Bell as telling the Cabinet meeting that Head Start pays off because it "makes taxpayers out of potential tax eaters." Brady said the jobs program was deemed a bargain, particularly after Reagan saw the high minority unemployment in cities during his election campaign.

Moran indicated that although the Social Security benefit for the retired is protected, no final decision has been made on whether the minimum payment will be kept at its current level. A lowering of the minimum benefit is one often-proposed method of lessening the federal cost of Social Security.

On school lunches, Moran made clear that only the free breakfasts and lunches for poor children are guaranteed to escape the budget tax. The total outlays for school meals of all sorts, including partial payments for less needy children that have drawn fire from conservatives, are $3.6 billion in the Carter budget, $1.5 billion more than the core program Stockman has said does not need to be cut.

The protected veterans' benefits are only a portion of the $24 billion in outlays for veterans in the budget.

The Cabinet meeting on the economy came on a day when Reagan hosted governors and labor leaderrs in his continuing effort to secure support for his economic package.

Representatives of the governors emerged from their luncheon with Reagan expressing solid support. Gov. John Dalton of Virginia told reporters that not only Republicans such as himself, but Democrats, too, agreed that the president is on the right track.

The govenors said that they had not been told the specifics of where the federal spending cuts would come, but they were pleased to have been invited to form a liaison committee to OMB immediately and to be invited back to the White House for talks on Feb. 23, five days after Reagan is to annouce his proposed cuts.

Democratic George Busbee of Georgia went as far as any governor seemed to want to go yesterday in expressing concern about the impending cuts when he said that there will be differences between what the governors think can be cut and what the president thinks can be cut.

Reagan is to spend two or three more hours this week in Cabinet-level meetings on the budget, Brady said. During these meetings, Cabinet members will have the opportunity to protest cuts in their departments, he added.