Edward Lampert speaks during a news conference to announce the merger of Kmart and Sears in New York, Nov. 17, 2004.

Former Sears Chairman and CEO Eddie Lampert delivered a letter Thursday to presidential candidate Sen. Elizabeth Warren and Rep. Alexandria Ocasio-Cortez saying accusations that he has not paid severance to Sears employees laid off in the wake of the retailer's bankruptcy are based on "false" reports.

The employees in question have been paid, he says, according to a copy of the letter obtained by CNBC.

Lampert bought Sears out of bankruptcy last year through an affiliate of his hedge fund ESL Investments, Transform Holdco, after years of declines under his leadership as the retailer's CEO and chairman. The deal, which saved the company from liquidation, also promised that Lampert would reimburse Sears' severance costs for workers who lost a job in bankruptcy.

In their letter, Democrats Warren of Massachusetts and Ocasio-Cortez of New York accused Lampert of backing out of promises to Sears and to Warren in previous written exchanges.

"New reports of your efforts to avoid paying millions of dollars in severance payments to laid-off workers indicate that you are betraying the commitment you made to Sen. Warren, to the bankruptcy court, and most importantly, to the tens of thousands of workers who have lost their jobs and face uncertain futures after your exploitative tenure at Sears," the two wrote.

Lampert's reply says those reports were misinformed.

Lampert has been arguing with Sears over the terms of his purchase agreement to buy the company out of bankruptcy. He describes the fight as one between now defunct "Old Sears" and post-bankruptcy "New Sears." Both sides believe the other has not delivered on the terms of their agreement that was quickly put together to keep the company alive.

Lampert has said in court filings he believes "Old Sears" has failed to hand over "New Sears" certain inventory and property at Sears' Illinois headquarters, as promised. To cover that shortfall, he is requesting approval from the bankruptcy court judge for "New Sears" to not reimburse "Old Sears" for its severance costs, as originally agreed. The costs, originally estimated at $43 million, are now pegged closer to $20 million.

Lampert said whether he reimburses Old Sears for those costs has nothing to do with whether employees get paid, an event he says has already occurred.

"This is entirely an issue between Old and New Sears," Lampert's letter said.

"To our knowledge, the eligible employees whose employment was terminated by Old Sears prior to our acquisition have received all severance due to them."

In a statement, Sen. Warren and Rep. Ocasio-Cortez said, "Eddie Lampert can quibble over whether he stiffed Sears workers directly or whether he stiffed Sears' workers as creditors, but the bottom line is that his leadership cost thousands of workers their jobs and millions of dollars. They deserve answers."

Lampert defends his tenure running Sears. Under his leadership, the owner of Sears and Kmart suffered years of losses, store closures and layoffs. Lampert, as its largest shareholder, also struck several deals including its spinoff of Lands' End in 2014 and carved out many of its best properties into Seritage Growth Properties, a real estate investment trust Lampert created a year later.

Those deals are now under scrutiny in a lawsuit Sears filed against Lampert other past board members, alleging the transactions were akin to "theft." Warren and Ocasio-Cortez referred to some of those allegations in their previous letter to Lampert.

Those allegations, said Lampert, are undeserved.

"Unlike many other situations where private equity owners simply allowed companies to fail, ESL supported the company for years," his letter said. "Sears' employees, pension plans and trade creditors are all much better off because of the efforts we made, and continue to make, to keep the business going. And, ESL is not in the business of 'making short term profits.'"

Lampert referred Warren and Ocasio-Cortez to challenges, store closures and layoffs by other major retailers, including Macy's, J.C. Penney and Toys R Us.

"Singling Sears out and publicly disparaging me and the company because we were not able to successfully transform Old Sears, when so many others have met a similar fate, is unfortunate and unfair," wrote Lampert.

"You have made harsh charges on the basis of allegations made in lawsuits and other court filings that have not been adjudicated and have accepted at face value claims that have been thrown about in years of slanted media coverage."

Read the full text of Lampert's letter sent Thursday here: