Duke Energy and a hedge fund continued a public battle Monday about the financial performance of the utility, including the operations of Duke Energy Florida.

The West Palm Beach-based Elliott Investment Management L.P. sent an 11-page letter to the Duke Board of Directors criticizing company leaders and saying Duke Energy Florida is “perhaps the most glaring example of under-management.”

“Duke’s customers and investors deserve a thorough, unbiased analysis of whether Duke Energy Florida’s operations can be optimized to lower operating costs, increase grid investment and enhance reliability,” said the letter, which described Elliott as one of Duke’s largest investors.

But Duke fired back at the hedge fund, which in May called for the possibility of breaking off Duke Energy Florida into a standalone utility. In a statement Monday, Duke said Elliott “has again failed to provide any concrete and specific ideas to increase shareholder value, choosing instead to launch public attacks supported by cherry-picked data and anonymous sources.”

“Duke Energy will continue running the business in the best long-term interests of all shareholders and stakeholders, and not those of a single hedge fund focused only on the short term and with a decidedly mixed track record in its other interventions in the utility sector,” the North Carolina-based utility said in the statement.

The statement also said the hedge fund’s idea of breaking up the company “collapsed immediately because it was financially unsound and ran counter to the strategic direction of the entire industry.”

“Over the past several months, Duke Energy’s management team has been in active dialogue with the equity analyst community and institutional shareholders,” the Duke statement said. “Our largest investors, as well as analysts, public officials and other stakeholders were near universal in their rejection of the hedge fund’s unsound plan.”

But Elliott in Monday’s letter again raised the possibility of breaking off Duke subsidiaries in Florida and the Midwest into standalone utilities. It said Duke Energy Florida compares unfavorably to Florida Power & Light and Tampa Electric Co. on measurements such as customer rates and reliability.

“The same strategies employed by Duke’s high-performance peers in Florida and the Midwest could be applied to Duke’s utilities, and we believe the fastest, clearest and highest confidence path to high grade these utilities is through separate, focused ownership,” the letter said. “Our conversations have uncovered a wide range of perspectives on potential paths that Duke could pursue to unlock value, all of which warrant further independent exploration.”

Duke Energy Florida is the second-largest utility in Florida, with more than 1.9 million customers, trailing only FPL. It was created after Duke merged with Progress Energy in a deal that was completed in 2012.

In addition to targeting the operations of Duke’s Florida and Midwest subsidiaries, Elliott also is calling for steps such as increasing the independence of the utility’s board. But Duke pushed back against the criticism.

“Elliott’s attempt to undermine Duke Energy’s leadership team ignores the diverse and experienced professional talent that drives this company and is silent on the significant accomplishments it has achieved,” the utility said in its statement Monday.