MG Capital, run by former Third Point executive Michael Gorzynski, said for the second time in two months that it wants Falcone out. Gorzynski asked lead independent director Wayne Barr in a letter seen by Reuters a "to facilitate the removal of Mr. Falcone."

In February the fund, which owns 5% of HC2 along with its partners, criticized the company's financial performance and said it wanted to replace the entire board, including Falcone, with six directors of its own.

Now, Gorzynski is focusing more on Falcone, whose bets on the overheated housing market at his Harbinger Capital turned him, briefly, into a billionaire. Last year his net worth was closer to $300 million, he told lawyers.

"Based on Mr. Falcone's well-documented financial, legal and regulatory issues, MG Capital - and presumably other stockholders - remains perplexed by the incumbent Board's focus on preserving HC2's status quo," MG Capital said in the letter.

HC2 has businesses in construction, marine services and several other sectors. A spokesman for the firm was not immediately available for comment.

An MG spokesman confirmed the content of the letter.

In the last six weeks, Falcone has been sued for more than $65.8 million for allegedly defaulting on loans and had his assets frozen for failing to pay lawyers. Last year HC2 was ordered by a court to withhold some of Falcone's wages to satisfy unpaid obligations after he was ordered to pay New York City $2.69 million in unpaid taxes.

"We remain deeply troubled by the impact that Mr. Falcone's apparent financial distress and legal issues may have on HC2," MG Capital said.

In papers filed Feb. 21 with the New York State Supreme Court in Manhattan, Melody Business Finance LLC said Falcone and affiliates reneged on obligations to repay loans, which date from 2013 to 2017, and improperly sold some of the underlying collateral, including an Andy Warhol painting.

Alex Spiro, a partner at Quinn Emanuel Urquhart & Sullivan representing Falcone, said in an statement: "This is a personal dispute without merit. We will fight this."

In early March, Justice Arthur Engoron froze Falcone's assets after he failed to pay $13.6 million to law firm Dontzin Nagy & Fleissig.

The firm represented Falcone in 2013 when he settled allegations with the Securities and Exchange Commission that he borrowed $113 million from his hedge fund to pay personal taxes and gave preferential treatment to certain clients when he halted redemptions.

Gorzynski in the letter to Barr said MG would "engage in a constructive one-to-one dialogue with you and the other directors once Mr. Falcone has been removed."

(Reporting by Svea Herbst-Bayliss; Editing by Christopher Cushing)