New Jersey's Passaic River and the Newark skyline in 2011.

The state of New Jersey is pushing forward with a seven-year-old civil lawsuit against YPF subsidiaries Maxus Energy Corp. and Tierra Solutions for their ties to a pesticide plant that dumped dioxin, a highly toxic chemical and suspected carcinogen, into the Passaic River in the 1950s and 1960s. Maxus's predecessors owned the plant until 1986 and Tierra was created to deal with the plant's legal liabilities.

New Jersey's Passaic River as it looked in Paterson in 1859. An EPA estimate has put the cleanup cost of a polluted eight-mile area of the river at $1 billion to $3.4 billion.

The state is going after YPF for compensatory and punitive damages. In court documents it has said the dioxin damaged not just the river but the local port industry, commerce, public and private property, wildlife and the state's natural resources.

"Basically, the state is seeking any and all Passaic River-related remediation costs that it may bear from Maxus, Tierra and their related entities, in addition to past costs and damages the state has suffered as a result of the dioxin contamination in the river," said Lee Moore, a spokesman for the New Jersey attorney general's office.

New Jersey officials say the concentration of dioxin in the river's fish and crabs is among the highest reported in the world and continues to endanger people and wildlife. Consumption of river crabs has been banned for decades.

The attorney general's office in Trenton is following up state court rulings in 2011 and 2012 that found Maxus and Tierra liable for polluting the river, which flows through the northern part of the state, including the city of Newark. New Jersey claims the defendants for decades "orchestrated and implemented a strategy to delay and impede the cleanup and restoration of the Passaic River."

YPF declined to comment on the case. It has argued in court documents that the river's "longstanding and widespread pollution...cannot plausibly be blamed on the operations of a single manufacturing facility."

The pesticide plant, which is located in Newark and produced the Vietnam War-era defoliant Agent Orange and DDT along the river banks, was shut down several decades ago. What remains of it is entombed in concrete and covered in pebbles.

When YPF bought Maxus in 1995, it acquired not only its oil fields but also its legal liabilities including those stemming from the chemical plant.

Though YPF has already been found liable for the cleanup costs, those costs have yet to be determined and the trial is now in a phase that could also add punitive damages. Mr. Moore said this phase of the trial is on hold while the state addresses the possible involvement of hundreds of other companies, city governments and state agencies in polluting the river. Those parties, who were named in a countersuit by YPF, could also be held liable for some compensatory cleanup costs and punitive damages.

"However, we anticipate proceeding with the damages phase against these defendants as expeditiously as the court will allow," Mr. Moore said, referring to Maxus and Tierra.

Last May, Argentina's government expropriated a 51% stake in YPF from Spain's oil firm Repsol SA, REP.MC +2.55% which means the government may now be on the hook for damages that Repsol might have been required to pay. Repsol declined to comment.

In 2009, in a bid to spread the cleanup costs, YPF filed a countersuit against the state and claimed that around 300 other companies, municipal governments and public entities, such as sewage facilities, also polluted the river and should help fund its cleanup.

One of those towns, Linden, is about 13 miles south of the plant. Linden Mayor Richard Gerbounka says the city had nothing to do with the dioxin poisoning. "This makes no sense," he said. "It's very frustrating to have to spend taxpayer dollars on lawyers' fees to defend ourselves for something that we had no role in doing in the first place," he said.

Many of the defendants named by YPF, including Linden, which is trying to limit its potential legal bills, have reached a tentative settlement to pay some of the cleanup costs. The settlement requires court approval. But if it is approved, the court could dismiss YPF's countersuit claims, leaving the company to foot more of the cleanup bill.

Separately, the U.S. Environmental Protection Agency has identified around 70 companies that in some way polluted the river and they have agreed to pay for an EPA-led cleanup study of part of the Passaic. EPA officials are hopeful the companies will also help pay for the cleanup itself, though it remains unclear how this would happen.

"A lot of companies polluted the Passaic River for hundreds of years," said Elizabeth Butler, an EPA manager involved in the cleanup project. "They have to fight it out and decide who has to pay how much. Trying to guess what their share of the cost will be at the end of the day is anybody's guess."

Meanwhile, some of the defendants named by YPF, including around a dozen towns, are also urging state legislators to pass a bill that would shield taxpayers from the cleanup costs by ensuring that towns and public entities aren't held liable. Supporters of the bill say cleanup costs for the Passaic and Newark Bay area could cost tens of billions of dollars.

Christopher Hartwyk, an attorney for some of the defendants, said if the bill became law, it could protect cities and other public-sector defendants such as sewage facilities from YPF's claims, leaving the company to pay more.

Over the years, the pollution has spread to include a 17-mile stretch of the river and surrounding areas. A recent EPA estimate puts the cleanup cost of an eight-mile area of the river at between $1 billion and $3.4 billion, not including punitive damages the state could seek from YPF. Cleaning up the entire 17-mile area could raise that amount significantly.

"The New Jersey government estimates the environmental damage to be around $3 billion, which YPF is going to end up paying for now. It is negotiating that now," said a member of YPF's board of directors. It is unclear if YPF expects to pay any punitive damages on top of this.

Jeff Tittel, director of the New Jersey Sierra Club, an environmental group, says dioxin caused the worst damage and that Maxus and Tierra are most responsible for it. The state says the dioxin is "clearly traceable" to the pesticide plant. Mr. Tittel said his aunt and uncle lived three blocks from the plant, and that both died from liver cancer as a result of dioxin poisoning.

EPA officials say cleanup costs could vary substantially depending on how much of the river sediment is dredged and where it is stored. The cleanup could easily take over a decade.