DAVENPORT, Iowa — Sen. Bernie Sanders proposed a tax on the wealthiest Americans on Tuesday as a way to help underwrite his slate of ambitious — and costly — policies, offering his own version of an idea one of his toughest rivals has campaigned on aggressively and pushing it further.

The Democratic presidential candidate, an independent from Vermont, offered his blueprint after Sen. Elizabeth Warren (D-Mass.), who has surged in the polls, made a wealth tax one of her signature ideas. Her crowds regularly chant “Two cents!” at her rallies when she brings up the idea, a reference to how much the wealthy would have to pay on the dollar.

Sanders’s proposed wealth tax is more aggressive than Warren’s and would raise more money. Warren’s plan calls for levying a 2 percent tax on wealth above $50 million, as well as a 3 percent tax on wealth above $1 billion. The relatively high threshold has helped Warren fend off critiques that large farms could be exposed to the tax.

Sanders would hit more people with the tax and would also significantly increase how much it would take from the very wealthiest, following a pattern in which he has sought to stake out the leftward boundary of the Democratic Party when it comes to policy proposals.

Sanders’s plan introduces a new 1 percent wealth tax on those earning over $32 million and then increases that rate in steps until it reaches 8 percent for those with more than $10 billion.

The announcement Tuesday highlighted the country’s striking divide over economic policy. Two of the three top-polling candidates for the Democratic nomination are now advocating a sweeping change in the way wealth is allocated in the United States, embracing policies that have not been so prominently discussed since the 1960s.

Under President Trump, meanwhile, the Republicans have passed a far-reaching tax cut plan that economists say will dramatically expand the deficit. This comes less than a decade after the tea party angrily seized the nation’s attention, and a measure of power within the GOP, with a low-spending, anti-deficit message.

On Tuesday, Sanders concluded a two-day swing through Iowa counties that Barack Obama won and then went for Trump. He’s dubbed the trip his “Bernie Beats Trump” tour, presenting himself as the most electable Democratic candidate against the president.

But Sanders has struggled to recapture the magic of his near-win in this first caucus state in 2016. A recent Des Moines Register/CNN/Mediacom poll showed Warren leading with 22 percent. Former vice president Joe Biden was at 20 percent, and Sanders was running third at 11 percent.

Sanders and Warren have been battling for supremacy in the Democratic Party’s liberal wing, issuing dueling proposals on a number of topics that would reshape the nation’s safety net and significantly expand the role of government.

Their proposals include making public colleges and universities tuition-free, wiping away much or all of the student loan debt in the country, and enacting a Medicare-for-all health-care system.

The plans are estimated to cost tens of trillions of dollars, raising questions about how they would be paid for. Warren for months has pointed to her wealth tax, and Sanders’s new proposal gives him a similar revenue source to cite.

Sanders aides noted that the senator has spoken of a wealth tax for decades, including proposing it as a possible funding source for his Medicare-for-all plan. In 1997, Sanders wrote that it was “time, high time, to establish a tax on wealth similar to those that exist in most European countries.”

However, there is no guarantee that Warren or Sanders, if elected, could push such a far-reaching new tax through Congress.

When it comes to wealth taxes, the impact on the nation’s biggest fortunes would be profound. Bill Gates, estimated to have $107 billion in wealth, would under Sanders’s plan pay at least an additional $8 billion annually to the federal government. Sanders’s campaign says the wealth of billionaires overall would be halved under his proposal.

The plan to tax the wealthy could pay for some of Sanders’s plans but fall short of covering other parts of his agenda. Economists Emmanuel Saez and Gabriel Zucman at the University of California at Berkeley estimate Sanders’s plan would raise $4.35 trillion over 10 years, although conservatives have said such estimates overstate how much can be raised through a wealth tax.

Sanders has unveiled a $2.5 trillion plan to end homelessness and create 10 million new housing units and a $1.7 trillion plan to cancel all student debt in the United States; those two initiatives alone would come close to equaling the money raised by the wealth tax. The campaign said the tax would be used to fund the housing plan, pay for universal child care and help finance Medicare-for-all.

The senator has proposed a $30 trillion Medicare-for-all health-care system that would eliminate families’ health-care spending, which Sanders has said would be paid for with higher middle-class taxes, as well as ­taxes on the wealthy.

The biggest difference with Warren’s plan is that Sanders’s would more directly target the fortunes of billionaires and multi­billionaires.

Zucman noted on Twitter that Sanders’s plan “would make it much harder to remain a multibillionaire durably.” But he said that if Sanders’s tax had been enacted in the 1980s, billionaires’ share of the national wealth would still have increased.

That means Sanders’s plan would stop short of a “maximum income” plan favored by some on the left, although Sanders has come out in favor of that as a long-term goal, telling the New York Times, “I don’t think that billionaires should exist.”

That position follows months of debates in left-leaning circles over whether Democrats should push taxes high enough to eliminate all billion-dollar fortunes, an idea championed, for example, by an aide to first-term Rep. Alexandria Ocasio-Cortez (D-N.Y.).