TRENTON, N.J. — Merck & Co. will pay $671 million to settle claims it overcharged government health programs for four popular drugs and gave doctors fees and gifts to induce them to prescribe its drugs, U.S. prosecutors and company officials said today.

The alleged overcharges, dating back to the mid-1990s, involved Medicaid programs in all but one state and the District of Colombia, as well as federal health-insurance programs at agencies including the Public Health Service, Department of Defense, and Veterans Administration.

A nationwide investigation by federal prosecutors, triggered partly by a former Merck salesman-turned-whistleblower and a Louisiana doctor who exposed part of the alleged overcharging, resulted in two settlements announced today.

In Philadelphia, U.S. prosecutors said Merck agreed to pay $399 million plus interest for improper calculation of Medicaid rebates and its marketing practices. And in New Orleans, the U.S. Attorney’s office said the drugmaker agreed to pay $250 million plus interest for its rebate practices.

The interest payments boost the total payout to $671 million, Merck said.

The company said the settlements do not constitute an admission of any liability or wrongdoing.

“What we have here is a disagreement (over) the rules of the Medicaid rebate program,” a Merck spokesman, Ronald Rogers, said. “These civil settlements were the best and most appropriate way to resolve these lengthy investigations and bring these matters to closure.”

Drug companies are required to report to the government the lowest price for their medicines to ensure that Medicaid programs get the benefit of the same discounts or rebates on the drugs they buy. Prosecutors said Merck, however, was hiding the steep discounts it gave to hospitals that used a set amount of Merck products and was reporting higher prices to the government.

Between 1997 and 2001, prosecutors said Merck also gave money and perks to doctors and other health care professionals to entice them to prescribe Merck drugs, a practice the government called excessive.

The Philadelphia case involved pricing programs for the cholesterol drugs Zocor and Mevacor and the painkiller Vioxx, which Merck pulled from the market September 2004 because Vioxx doubled risk of heart attack and stroke. Those programs ran from 1996 through 2006, a Merck spokesman, Ron Rogers, said.

The Louisiana case involved pricing for the heartburn drug Pepcid, from mid-1996 to April 2001, when it was still sold as a prescription drug.

“At the time that these pricing programs were in place, Merck believes that it acted in good faith and complied with the regulations that were in place at the time,” Mr. Rogers said.

When Merck reported its fourth-quarter financial results on January 30, they included a $671 million charge for the anticipated resolution of federal and state civil probes into past sales and marketing practices.

At the time, lawyers for Merck, federal prosecutors, and a senior U.S. District Court judge, Lewis Pollak, were meeting weekly to finalize the agreement.

In afternoon trading today, Merck shares rose 13 cents to $45.83, near their 52-week low of $42.32.