Elizabeth Warren has stepped up her attack on the billionaires opposing her proposals for a new “wealth tax” by launching a scathing new ad that targets four of America’s richest men by name.

In the ad, Elizabeth Warren Stands Up to Billionaires, to be broadcast on US TV this week, the leftwing Massachusetts senator trains her sights on the investor Leon Cooperman, the former Ameritrade CEO Joe Ricketts, the former Goldman Sachs CEO Lloyd Blankfein and the investor Peter Thiel.

“It is time for a wealth tax,” Warren proclaims at a campaign rally in a high school gym to the cheers of students. “I’ve heard there are some billionaires in America who don’t support this plan,” she adds faux-incredulously, before identifying four of her least favorite billionaires, along with their alleged wrongdoings or opposition to her tax proposal.

Cooperman, who the ad notes settled with the Securities and Exchange Commission in 2017, paid nearly $5m in fees over insider trading violations and recently teared up during a TV interview on the subject of his wealth, has previously slammed Warren.

The senator, Cooperman told CNBC, “represents the worst in politicians as she’s trying to demonize wealthy people because there are more poor people than wealthy people”.

Cooperman, who recently sent an open letter to Warren claiming her treatment of him was like “a parent chiding an ungrateful child”, is not the only billionaire hitting back at Warren’s proposal to pay for universal health insurance by imposing a 2% tax on net worth between $50m and $1bn and a “super-tax” of 3 cents on every dollar of wealth over $1bn.

Cooperman also referred directly to Warren’s heritage claims, which have included her citing her race as “American Indian”.

“Why did you lie on your Texas bar application in 1986?” Cooperman asked. “We don’t need another fabricator in the White House.”

The ad appeared to touch a nerve with Blankfein, who tweeted he was “surprised” to be featured in it and also included an insulting reference to a scandal over Warren’s prior claims of Native American ancestry. “Maybe tribalism is just in her DNA,” his tweet said.

The probable 2020 contender and billionaire businessman Michael Bloomberg has described the plan as anti-capitalistic. After he registered for the Democratic primary in Alabama, Warren tweeted him her online calculator for billionaires to determine how much of his $51bn fortune would be taxed under her increased rate.

The super wealthy appear to be taking Warren’s attacks seriously. Bill Gates recently said he had started to “do a little math” on how much he might be taxed, saying he has already paid more than $10bn, while Mark Zuckerberg has described Warren as an “existential” threat.

Mark Cuban, the Dallas Mavericks owner, whose net worth is estimated at about $4bn, has accused Warren of being “intellectually dishonest” by “selling shiny objects to divert attention from reality”.

JP Morgan’s CEO, Jamie Dimon, has also waded into the feud, saying Warren uses “harsh words” and appeared to vilify successful people. “I don’t like vilifying anybody,” Dimon said. “I think we should applaud successful people.”

But Warren’s potential nomination could cause Democratic donors on Wall Street to sit out the election – or support Donald Trump.

Warren has responded that she was unfazed by the potential loss of wealthy supporters.

“I’m fighting for an economy and a government that works for all of us, not just the wealthy and well-connected,” she has tweeted. “I’m not afraid of anonymous quotes, and wealthy donors don’t get to buy this process. I won’t back down from fighting for the big, structural change we need.”