In one of the Reagan administration's biggest internal budget blowups so far, officials in the Department of Housing and Urban Development have roundly denounced new spending cuts proposed by the president's budget office, saying "there is simply no way to disguise this attempt to 'balance the budget on the backs of the poor.' "

The officals, in a draft appeal of the proposed cuts prepared for HUD Secretary Samuel R. Pierce Jr., warned that some of them, in public housing programs, could lead to "rent strikes, riots, vandalism and irreparable damage to projects," as well as "litigations, bankruptcy and receivership" in some instances.

Sources said the draft language, including the references to riots and balancing the budget "on the backs of the poor," was later toned down by Pierce and aides before the appeal was sent on to the White House. The precise final language was not immediately known, but the sources said some of the most inflammatory statements in the draft were altered.

The draft appeal says other contemplated budget cuts, including some in programs that provide housing to the elderly or mortgages in rural areas, are simply foolish politically.

"The political support for a number of these beneficiary groups is incredibly strong, and it is foolish to antagonize organizations which would normally be strong supporters of the administration by engaging in a battle where the political losses will inevitably be far greater than any foreseeable outlay savings," the department wrote in its draft.

In a reference that was subsequently deleted, the appeal said other proposals by the Office of Management and Budget are "offensive and juvenile." In its final language, it describes still another OMB proposal as "an attempt to renege on valid existing contracts and to try to reverse the government's valid commitment to helping the very poor find decent housing."

OMB's proposed cuts in the HUD budget for fiscal 1983, which begins next Oct. 1, have been leaking out for several days. They are among cuts the budget office is proposing all across the government to reduce the projected deficit in the spending plan the president will submit to Congress in January. Some experts say that deficit will now exceed $100 billion.

The largest proposed cuts would be in the government's various subsidized housing programs for the poor. These now cost more than $8 billion a year and are the government's fastest growing and third largest welfare program, behind Medicaid and food stamps.

These housing programs have steadily expanded over recent years; OMB has proposed that this expansion be abruptly halted. It would also appreciably increase the amount of rent that low-income families who receive this assistance would have to pay.

New such reductions came to light in a summary of the OMB proposals and HUD's appeal that leaked out yesterday. OMB would slash operating subsidies for public housing from 75 percent of need in 1982 to 25 percent in 1983 and would require local housing authorities to make up the difference by raising tenant rents.

Some 1.2 million households live in public housing projects. The government now pays 75 percent of the operating or maintenance cost of these projects; the rest comes mainly from rents. It is this government contribution OMB would cut back to 25 percent.

OMB would also count food stamps in figuring the incomes of subsidized housing tenants. Their rents are fixed percentages of their incomes; counting food stamps as income would make them pay more.

The documents made available yesterday also indicate that OMB wants to cut far more than previously disclosed from HUD's programs to provide mortgage money to moderate-income families.

OMB proposes that the Federal Housing Administration insure mortgages only for those families that cannot be served by the private mortgage insurance industry. This is a proposal that the President's Commission on Housing had considered and that the private insurers have been pushing for some time.

Even the private insurers, however, have not thought it would be possible to make such a radical shift to the private sector all at once and have suggested a more modest transition.

The minimum-level approach to FHA would "give a clear signal that this administration intends to abandon the housing industry and ignore the plight of young home buyers," the appeal said in response to the OMB proposal.

HUD already had proposed elimination of any new funds for construction of low-income housing and wanted to start the process toward a substitution of housing vouchers--grants to individual families--as the main federal housing subsidy for the poor.

But OMB went a step further and wanted to shift to the voucher system about 200,000 apartments at about half the subsidy level given currently. HUD believed that a tax-exempt financing plan it proposed for funding multi-family housing construction would help offset the end of Section 8 construction, but OMB cut that plan out too.

"At a time when the housing industry is at an all-time low, when construction unemployment has reached depression levels, the OMB would eliminate current housing programs without offering any alternative vehicle for providing assistance," the appeal concluded.

OMB proposes not only to block further additions for low-income housing but to rescind earlier budget authority for about 150,000 units. This way it actually ends up with negative budget authority for the next four years and greatly reduced outlays to make up for past obligations.