New York state, Massachusetts and Maryland are suing Volkswagen and its affiliates Audi and Porsche over diesel emissions cheating, alleging that the German automakers defrauded customers and violated state environmental laws by selling diesel vehicles equipped with software allowing them to cheat emissions testing.

The lawsuits, announced Tuesday, allege that Volkswagen and its affiliates sold tens of thousands of vehicles with so-called "defeat devices" installed.

The New York complaint accuses company employees of trying to cover up the cheating by submitting false documents to state officials and destroying incriminating paperwork.

"The allegations against Volkswagen, Audi and Porsche reveal a culture of deeply-rooted corporate arrogance, combined with a conscious disregard for the rule of law or the protection of public health and the environment," said New York Attorney General Eric Schneiderman. "These suits should serve as a siren in every corporate board room, that if any company engages in this type of calculated and systematic illegality, we will bring the full force of the law — and seek the stiffest possible sanctions — to protect our citizens."

Top VW executives, including former CEO Martin Winterkorn, knew about the deception, the New York lawsuit alleges, and participated in efforts to cover it up.

In a statement, Volkswagen said it is already in talks with authorities regarding "a comprehensive national resolution of all remaining environmental issues arising from the diesel matter." The company also noted that it has agreed to buy back or modify affected vehicles, create a $2.7 billion environmental trust and invest $2 billion on infrastructure for zero-emission vehicles.

"The allegations in complaints filed by certain states today are essentially not new and we have been addressing them in our discussions with U.S. federal and state authorities," the company said. "It is regrettable that some states have decided to sue for environmental claims now, notwithstanding their prior support of this ongoing federal-state collaborative process."

The legal action seeks "substantial penalties" that would be based on a calculation of the duration of the alleged violations.

Schneiderman and his Massachusetts counterpart, Maura Healey, detailed the case at a Tuesday news conference in New York City. The two Democrats are the top law enforcement officials in their respective states, and each state will file its own lawsuit.

The suit comes after the German automaker agreed to spend up to $15.3 billion to settle consumer and government lawsuits over the emissions cheating, first disclosed in 2015.

Schneiderman and Healey say that settlement did not resolve claims regarding violating state environmental laws and did not cover all the affected vehicles.

"With today's action, we want to make clear to all auto manufacturers that violating laws designed to protect our environment and our public health is unacceptable and will be punished with significant penalties," Healey said.

Maryland officials announced their lawsuit separately.

"Their disregard for the health of our citizens and their disregard for our environment must be punished," Maryland Attorney General Brian Frosh said in a statement.

The suit alleges that Volkswagen and Audi, followed by Porsche, began installing the cheating software in more than a dozen U.S. models beginning in 2008. The software was designed to alter the emissions system during government testing to ensure nitrogen oxide emissions were within allowable limits.

Some 25,000 affected vehicles were sold in New York state and 15,000 in Massachusetts, according to the lawsuits. As of October, about 13,000 such vehicles were registered in Maryland, officials said. Some 600,000 were sold across the country.

The prosecutors say consumers who purchased one of the vehicles believed they were buying a "green diesel" car, even though the vehicles illegally emitted pollutants linked to respiratory disease, elevated ozone levels and smog.