President Reagan last night appealed to Americans for radical changes in the nation's tax code, promising to replace a system that has become "unwise, unwanted and unfair" with lower rates and "a future of greater growth and opportunity for all."

In a nationally televised address from the Oval Office that launched the major political initiative of his second term, Reagan vowed to "free us from the grip of special interests" by eliminating many tax breaks, while providing new tax relief to the poor, families and the great swath of middle-income taxpayers.

"I'll start by answering one question on your minds. Will our proposal help you? You bet it will," Reagan said. "We call it America's tax plan, because it will reduce tax burdens on the working people of this country, close loopholes that benefit a privileged few, and simplify a code so complex even Albert Einstein reportedly needed help on his 1040 form . . . . "

In the official Democratic response, House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) gave a strong, if qualified, endorsement to Reagan's call for tax simplification. But two congressional advocates of comprehensive tax change, Reps. Jack Kemp (R-N.Y.) and Richard A. Gephardt (D-Mo.), said they oppose the president's proposal. Reagan said the tax debate "should not be a partisan debate."

Reagan's address put a strong emphasis on the tax cuts that would result from his proposal, while minimizing the effect on individuals and businesses that would have to shoulder a higher tax burden, saying they were only being asked to pay "their fair share."

Although he cast his proposal as one directed at "Main Street America," the Reagan plan would be far more generous to certain industries and wealthy individuals than the tax revision proposal offered last year by the Treasury Department. The president made no mention of the original Treasury plan.

The new plan would provide the greatest tax rate reductions for the poorest and wealthiest taxpayers.

Overall, when measured against the current tax code, Reagan's proposal would represent a shift in tax burdens from individuals to corporations. The administration estimated that Reagan's plan would raise total corporate tax payments by 9 percent while lowering total individual tax payments by 7 percent.

Reagan proposed reducing the current 14 tax brackets to three brackets: 15 percent, 25 percent and 35 percent. There would be zero tax on the first $4,000 of taxable income on a joint return. The 15 percent bracket would apply to taxable income from $4,000 to $29,000 on a joint return, the 25 percent bracket to income between $29,000 and $70,000 and the 35 percent bracket to income above $70,000. The top tax rate would be reduced from 50 percent.

Reagan also proposed nearly doubling the personal exemption from $1,040 this year to $2,000 next year. He also proposed increasing the earned income tax credit from $550 to a maximum of $726, and he proposed increases in the zero bracket amount. He said the plan would increase the amount of tax-deferred contribution to a spouse's individual retirement account (IRA) from $250 to $2,000.

In exchange for reduced rates, Reagan proposed eliminating or curtailing many current tax breaks, including the deduction for state and local taxes and the "marriage penalty." He would retain the mortgage interest deduction for principal residences but limit other interest deductions.

Reagan also proposed allowing continued deductions for charitable contributions for those who itemize but would eliminate it for those who do not.

He said deductions for medical expenses would be preserved and deductions for casualty losses continued, as would be the current preferential treatment of Social Security benefits and veterans' disability payments.

The plan would eliminate the tax break for business expenses and limit the deduction for business meals and travel expenses, continue special treatment of capital gains income and impose limited taxes on employes' fringe benefits, while unemployment compensation would be fully taxed.

The plan would reduce the existing 46 percent top tax rate on corporations to 33 percent, allow corporations to deduct 10 percent of the dividends they pay, eliminate the investment tax credit and revise the accelerated depreciation system, a central feature of Reagan's 1981 tax cut.

Reagan also proposed to "retain and tighten" the current minimum tax on individuals and corporations.

The White House said Reagan's proposal would ensure that "virtually all families at or below the poverty line would be freed from taxation," and would "assure that virtually all older, blind, or disabled Americans at or below the poverty line would be freed from taxation."

A White House chart showed that those with incomes of less than $10,000 a year would get a rate cut of 35.5 percent; those between $10,000 and $15,000, a 22.8 percent rate cut; those between $15,000 and $20,000, a 13.5 percent rate cut; those between $20,000 and $30,000, a 8.7 percent rate cut; between $30,000 and $50,000 a 6.6 percent rate cut; between $50,000 and $100,000, a 4.2 percent rate cut; between $100,000 and $200,000, a 4.1 percent rate cut, and for more than $200,000, a 10.7 percent rate cut.

Reagan's proposal would decrease taxes for 58.1 percent of families, raise them for 20.7 percent and leave the remaining 21.2 percent unchanged, the White House said.

In his address, Reagan said his proposal would simplify a tax code that has become "complicated, unfair, cluttered with gobbledygook and loopholes designed for those with the power and influence to hire high-priced legal and tax advisers."

He said the number of taxpayers who itemize would be reduced to one in four, but a White House summary said it would be one in three. Currently, about 37 percent itemize.

Reagan said a voluntary "return-free system" would be established to allow taxpayers to have their taxes automaticaly figured by the Internal Revenue Service. "We believe that most Americans would go from the long form or short form to no form," Reagan said.

"Comparing the distance between the present system and our proposal is like comparing the distance between a Model-T and the space shuttle," he added, "and I should know, I've seen both."

Reagan devoted much of his address, in which he used colorful graphic displays, to extolling the virtues of his proposal for families and average-income taxpayers, key constituencies for which both political parties are vying.

Reagan advertised his proposal as "the strongest pro-family initiative in postwar history," as a "ladder of opportunity" so the poor can "climb out of poverty forever," as creating "millions of new jobs for working people" and an "opportunity for everyone to hitch their wagon to a star and set out to reach the American dream."

Reagan's proposal is designed to be "revenue neutral," meaning that it would raise approximately the same amount of revenue as current law and thus would not aggravate the federal deficit. But Reagan repeatedly stressed that it would be a tax cut for many people. "We want to cut taxes, not opportunity," he said.

He said "the power of these incentives would send one, simple, straightforward message to an entire nation: America, go for it."

But Reagan said those who would have to pay more are doing so out of "fairness" to others. "Restoring confidence in our tax system means restoring -- and respecting -- the principle of fairness for all," he said.

"There is one group of losers in our tax plan -- those individuals and corporations who are not paying their fair share, or, for that matter, any share," Reagan said. "These abuses cannot be tolerated. From now on, they shall pay a minimum tax. The free rides are over."

But the president also sounded defensive about some aspects of the plan that make concessions to special interests.

For example, in making the final decisions on the plan, Reagan agreed to more generous tax breaks for the oil and gas industry than were envisioned in the first Treasury Department proposal. In his speech, he skipped over the first Treasury document and declared that the oil and gas industry "will be asked to pick up a larger share of the national tax burden" than under current law.

Reagan also defended the proposal to eliminate the state and local tax deduction, a key element in the plan because it represents a potential of about $34 billion in new federal revenue. The proposal has already drawn protests from leaders in high-tax states.

Reagan said two-thirds of Americans do not itemize so they receive no benefit from the deduction, but are being forced to "subsidize the high-tax policies of a handful of states."

"This is truly taxation without representation," Reagan said.