The members of Salo's group oversee state Medicaid programs, which split proceeds from the drug rebate program with the federal government. Medicaid, which provides health coverage primarily to low-income people, is jointly run by the federal government and individual states.

He added his group's members have been saying for months that Mylan's settlement with the Justice Department is "not sufficient."

"You've got to look back and say, 'How much they've been sticking it to us?' and [have Mylan] pony up," said Salo.

Matt Salo, executive director of the National Association of Medicaid Directors, said, "This is $1.27 billion that they absolutely do owe back to the government, who they've been ripping off."

"Mylan owes the American taxpayers $1.27 billion," he said. "It is time to collect."

"Mylan's outrageous multiyear classification has cost American taxpayers not just millions but billions," Blumenthal said. "The Department of Justice's deal is completely insufficient — a shadow of what it should be."

Blumenthal, D-Conn., at the same time blasted Mylan's purported settlement with the U.S. Justice Department for a mere fraction of that amount — just $465 million — to resolve claims that EpiPen was for years misclassified as a generic product for Medicaid's drug rebate program. Generic products are assessed a much lower rebate than brand-name drugs in that program.

Salo said that "this may be a great time to go back and say, 'Let's throw out this settlement.'"

Mylan has told CNBC for months that its agreement to pay the Justice Department $465 million is not finalized. The company announced the settlement, in which it admitted no wrongdoing, in October, after weeks of saying that it had properly classified EpiPen for purposes of the Medicaid drug rebate program.

New York City's comptroller, Scott Stringer, said, "These new allegations are simply shocking."

"If true, Mylan not only forced massive price hikes on consumers, but also overcharged American taxpayers more than a billion dollars for a life-saving drug," Stringer said. "At the same time, [Mylan's] board granted enormous pay packages to top executives. It's improper and it's immoral. Now, Mylan's shareowners are suffering the consequences. This is ultimately a Board failure — that's why investors are demanding change."

Stringer has oversight of New York City's pension fund. That fund, along with the pension fund of New York state, the California State Teachers' Retirement System and the Dutch pension fund PGGM, are jointly campaigning to have fellow Mylan shareholders reject the re-election of six company directors at Mylan's annual meeting June 22.

The quartet of funds are unhappy about, among other things, the fact that one director, Mylan Chairman Robert Coury, received almost $100 million in compensation last year, when the company was facing public outrage over its price hikes for EpiPen.

On Thursday, a Mylan spokeswoman declined to comment on Blumenthal's and Salo's demands for additional payments to Medicaid, other than noting that, "We continue to work with the government to finalize the settlement as soon as possible."

A Justice Department spokeswoman declined to comment.

Mylan's spokeswoman, when asked about the critique by pension funds, said, "Mylan's Board has overseen the development of a differentiated, clear and consistent long-term strategy that has created sustained long-term value for shareholders, while also serving the best interests of all stakeholders."

She noted that over the past 15 years, the market capitalization of Mylan had grown from about $3 billion to $20 billion, and that the stock price has risen by 140 percent in absolute terms. She said that almost all of Coury's compensation was granted and earned over his 15-year stint as CEO and then executive chairman.

"During Mr. Coury's long tenure, Mylan has delivered strong financial performance and shareholder growth, and his new compensation structure continues to be aligned with the company's stock performance," she said.

The demands for additional money from Mylan came after Sen. Chuck Grassley, R-Iowa, on Wednesday revealed the size of the potential underpayment to Medicaid for EpiPen.

The Senate Judiciary Committee, which Grassley is chairman of, had asked the inspector general's office of the federal Health and Human Services Department to calculate how much Mylan owed the Medicaid Drug Rebate Program if EpiPen had been classified as a brand-name product, instead of as a generic one.

Brand-name products are assessed higher rebate rates — at least 23.1 percent of sales — than the 10 percent rebate rate applied to generic drugs sold through Medicaid. But brand-name products whose prices are raised beyond the rate of inflation can pay a much higher rebate than that 23.1 percent.

Analysts have said that because of that, Mylan, which raised the price of EpiPen by more than 500 percent in recent years, could have owed Medicaid rebates that were nearly equal to the dollar amount of EpiPen sales through the program.

Mylan for years classified EpiPen, which treats potentially fatal allergic reactions, as a generic product. Federal health officials have said that they told Mylan it was misclassifying EpiPen, and that it should be treated as a brand-name product.

In a letter to the Judiciary Committee, the inspector general's office said it estimated the difference between what Mylan had paid Medicaid for EpiPen and what it could have owed if the auto-injector device was classified as a brand-name.

The office said that based on the methodology that it used, which had some limitations, "we determined the Estimated Rebate Differential to be $1.27 billion for 2006 through 2016."

The inspector general's office noted that it "did not determine whether Mylan's classification under the Medicaid Drug Rebate program was actually correct."

"Nor did we determine the amount of rebates, if any, the Federal Government should seek to recover now," the office said in its letter.

Mylan, in a regulatory filing in October, had said that it would begin paying Medicaid the higher brand-name rebate rate in April. But the company in March refused to say whether it was going through with that plan.