In an interview on CNBC, Cooperman tried to bring an end to his feud with Warren, saying he only wanted to talk about the stock market in future on-air conversations.
"But I'll go on record, if this lady wins, we're in big trouble," Cooperman said in the telephone interview on "Halftime Report."
"A wealth tax makes no sense," Cooperman said. "It would lead to unnatural acts, be near impossible to police, and is probably unconstitutional."
Cooperman's comments added to the public fight between the hedge fund pioneer and the Democratic senator, whose campaign rhetoric and tax proposals have drawn the ire of many on Wall Street and some of the nation's wealthy.
The back-and-forth intensified Wednesday, when CNBC reported that Warren's campaign would be running a new ad — on CNBC — that highlights her wealth tax proposal and criticizes billionaires, specifically calling out Cooperman and his past run-in with insider trading allegations.
Cooperman recently sent an open letter to the former Harvard professor, in which he claimed her treatment of him was like "a parent chiding an ungrateful child." He also teared up during a CNBC interview earlier this month, explaining that his outspokenness on the 2020 election is because "I care."
Cooperman was not the only billionaire featured in Warren's ad to respond Thursday. Former Goldman Sachs CEO Lloyd Blankfein tweeted that he was "surprised" to be included, in part because "we align on many issues."
Warren, whose campaign has sought to highlight growing income inequality in the U.S., is second to former Vice President Joe Biden in the RealClearPolitics average of national polls, while she narrowly leads the teeming field in an average of Iowa polls.
It's unclear what kind of "unnatural acts" Cooperman was referring to, but he suggested gold would be the "main beneficiary" as individuals seek to "hide their wealth."
Others have also questioned the constitutionality of Warren's proposal, which would place a 2% tax on household net worth over $50 million and a 6% tax on net worth over $1 billion. Even those who advised Warren on the plan aren't sure how the Supreme Court would rule.
Even so, billionaire investor Tom Steyer, who also is seeking the Democratic nomination, has proposed his own version of a wealth tax, at 1% annually on "the top 0.1 percent of American families," according to his website.
Cooperman has said he will support fellow billionaire Mike Bloomberg if the former New York mayor formally enters the race and maintains moderate policy positions.
Cooperman told CNBC last month that "if Elizabeth Warren is elected president, in my opinion, the market drops 25%."
Cooperman on Thursday reiterated his view and said there are other leading Wall Street titans who feel the same way, including Paul Tudor Jones.
The 76-year-old Cooperman also restated his openness to tax reform, claiming that he has "no problem paying higher taxes."
"You want to move me to 50% from 37% … that's fine," he said. "There's no better place to live than America, and I'll pay whatever taxes are asked of me."
But, he added, "what we have to do is work together, be serious students and understand."
Saloni Sharma, a spokeswoman for Warren's campaign, told CNBC in an email that during a Warren presidency, "We're going to tax Leon Cooperman's fortune of $3.2 billion."
"He can't escape the tax because it applies as long as he's an American citizen, and if he renounces his citizenship he'll have to pay a 40% exit tax on every dollar of his fortune above $50 million," Sharma wrote in response to Cooperman's remarks.
"We're going to be giving the IRS the teeth and the tools to make sure billionaires pay up," she added. "And this is all constitutional according to people who are actual constitutional law experts."
In recent years, Cooperman has mostly donated to Republican candidates, according FEC data, but he donated $1,000 to Hillary Clinton in 2016. He donated $2,700 to Jeb Bush and $2,000 to Sen. Marco Rubio earlier in the 2016 campaign cycle.
The son of a Bronx plumber who became one of Wall Street's most successful investors, Copperman started the Omega Advisors hedge fund in 1991. Last year, he returned outside investor money and converted Omega into a family office. Prior to starting Omega, he spent 25 years at Goldman Sachs.
Cooperman has also been a major philanthropist. He has signed The Giving Pledge, created by Bill and Melinda Gates and Warren Buffett. The Giving Pledge invites the ultra-wealthy to give away more than half of their fortunes to help society.
Correction: An earlier headline misstated Cooperman's quote. He said Warren's wealth tax proposal "is probably unconstitutional."