The proposal envisions slashing the tax rate paid by businesses large and small to 15 percent. The number of individual income tax brackets would shrink from seven to three — 10, 25 and 35 percent — easing the tax burden on most Americans, including the president, although aides did not offer the income ranges for each bracket.

Individual tax rates currently have a ceiling of 39.6 percent and a floor of 10 percent. Most Americans pay taxes somewhere between the two.

The president would eliminate the estate tax and alternative minimum tax, a parallel system that primarily hits wealthier people by effectively limiting the deductions and other benefits available to them — both moves that would richly benefit Mr. Trump. Little is known of Mr. Trump’s tax burden, but one of the small nuggets revealed in the partial release of a 2005 tax return this year was that he paid $31 million under the alternative minimum tax that year.

Corporations would not have to pay taxes on their foreign profits, an unusual proposal for a president who has championed an “America first” approach and railed against companies that move jobs and resources overseas. They would also enjoy a special, one-time opportunity to bring home cash that they are parking overseas, though administration officials would not say how low that rate would be or how they would ensure that the money would be invested productively.

Mr. Trump wants to double the standard deduction for individuals, essentially eliminating taxes on around $24,000 of a couple’s earnings. That proposal was met with alarm by home builders and real estate agents, who fear it would disincentivize the purchase of homes. The proposal would scrap most itemized deductions, such as those for state and local tax payments, a valuable break for taxpayers in Democratic states like California and New York.

But the president would leave in place popular breaks for mortgage interest, charitable contributions and retirement savings.

In a brief session with reporters, Mr. Cohn and Mr. Mnuchin said they had been toiling for weeks on the proposal, much of which closely resembles the plan Mr. Trump championed as a presidential candidate. They argued that it would spur robust economic growth that would — along with the elimination of deductions — cover the potentially multitrillion-dollar proposal entirely, a prospect that even many Republicans privately concede is virtually impossible.

“This will pay for itself with growth and with reduction of different deductions and closing loopholes,” Mr. Mnuchin said, repeating his optimistic estimate that the plan would spur the economy to grow at a rate of 3 percent annually. “The economic plan under Trump will grow the economy and will create massive amounts of revenues, trillions of dollars in additional revenues.”

Democrats rejected what they described as magical thinking behind the plan and condemned it as a giveaway to the rich masquerading as a tax overhaul.

“This is an unprincipled tax plan that will result in cuts for the 1 percent, conflicts for the president, crippling debt for America and crumbs for the working people,” Senator Ron Wyden of Oregon, the ranking Democrat on the Finance Committee, said in a statement. “Instead of providing a real tax reform plan as promised, this administration is offering cakes to the fortunate few.”

Bernard Baumohl, the chief global economist at the Economic Outlook Group, a forecasting firm, was unsparing.

“The effort to introduce more fiscal stimulus into the economy is genuinely underway,” he wrote to clients. “But the bare bones plan we saw unveiled today is already conceptually flawed and unlikely to go far in Congress. The final product will bear no resemblance to the principal points highlighted in today’s meager release. Certainly, the first step in this process was unimpressive.”

Mr. Cohn said the plan was “the most significant tax reform legislation since 1986” — the last time a comprehensive tax overhaul was enacted — as well as “one of the biggest tax cuts in American history,” in line with Mr. Trump’s grandiose portrayal.

As expected, the White House did not include in its plan the border adjustment tax on imports that was a centerpiece of a plan developed by House Speaker Paul D. Ryan of Wisconsin and Representative Kevin Brady, Republican of Texas and chairman of the Ways and Means Committee. Earlier on Wednesday, Mr. Mnuchin said the White House could not support that proposal “in its current form,” setting up an intraparty struggle over the elements of a tax plan and how to offset the deep reductions envisioned.

But Republican leaders who are eager for large tax cuts did not allow their internal divisions over elements of the package to obscure their overall support for Mr. Trump’s effort.

Mr. Ryan and Mr. Brady issued a joint statement with Senator Mitch McConnell of Kentucky, the majority leader, and Senator Orrin G. Hatch of Utah, the chairman of the Finance Committee, saying the principles outlined Wednesday would “serve as critical guideposts” as Congress and the administration worked together on a tax overhaul.

Mr. Trump also signaled support for revisions to the tax code that would help families with child-care costs, although his document provided no details. He called for ending the 3.8 percent tax on investment income that was imposed by the Affordable Care Act, restoring the capital gains rate to 20 percent.

Democrats are ready to battle Mr. Trump over the tax cuts, which they are determined to tie to his refusal to release his tax returns.

“Trump’s latest proposal is another gift to corporations and billionaires like himself,” said Thomas E. Perez, the Democratic Party chairman. “Trump must release his tax returns, as millions of Americans are demanding, before Congress can consider any Trump tax plan. We must know how much Trump would personally financially benefit from his own proposal.”

Questioned about that repeatedly on Wednesday, Mr. Mnuchin said that Mr. Trump, the first president in four decades not to disclose at least a portion of his tax returns, had “no intention” of releasing them now.

“I can’t comment on the president’s tax situation since I don’t have access to that, O.K.?” Mr. Mnuchin said when asked how large of a tax cut the president would receive under his own plan.

The plan contrasts starkly with the one championed by House Republicans, who proposed paying for their tax cuts in part with the new tax on imports, an effort to ensure that the measure would not swell the deficit.

The White House plan does call for “a territorial system to level the playing field for American companies,” akin to a component of House Republicans’ plan that would allow United States corporations to pay taxes only on their domestic profits.

“I worry that the Trump proposal would shift a tremendous amount of income abroad,” said Alan B. Krueger, who was a chairman of President Barack Obama’s Council of Economic Advisers. “It’s hard to square that with incentivizing investment in the U.S.”

Republicans have long called for permanent, comprehensive changes to the tax code, but lately they have shown increasing openness to tax cuts with an expiration date. If they embark on a plan to pass legislation that adds to the deficit and cannot be filibustered by Democrats, Senate budget rules dictate that the tax cuts would expire after a decade.

“If we have them for 10 years, that’s better than nothing,” Mr. Mnuchin said.

Democrats were particularly critical of Mr. Trump’s idea of allowing firms known as pass-through entities — including hedge funds, real estate concerns like Mr. Trump’s and large partnerships — that currently pay taxes at individual rates, which top off at 39.6 percent, to be eligible for the 15 percent corporate rate.

Critics worry that lawyers, doctors, consultants and other individuals in partnerships could structure much of their personal income as business income, effectively reducing their tax rate from 39.6 percent to 15 percent.

Mr. Mnuchin said the administration would not allow that to happen.

“We will make sure that there are rules in place so that wealthy people can’t create pass-throughs and use that as a mechanism to avoid paying the tax rate that they should be on the personal side,” he said.

The explanation did not seem to mollify Democrats.

“We don’t need a tax plan that allows the very rich to use pass-throughs to reduce their rates to 15 percent while average Americans are paying much more,” Senator Chuck Schumer of New York, the Democratic leader, said Wednesday. “That’s not tax reform. That’s just a tax giveaway to the very, very wealthy that will explode the deficit.”