WASHINGTON — The Supreme Court kicked off a new term Monday, with the justices wrestling with an attempt by oil companies to throw out lawsuits alleging they should pay damages for the impacts of climate change.

Although the case concerns a specific lawsuit the city and county of Boulder, Colorado, brought against Exxon Mobil and Suncor Energy, the ultimate decision could have broad ramifications for more than two dozen similar lawsuits brought by cities and counties around the country.

The justices — lacking a ninth member because Justice Samuel Alito’s recused — asked tough questions of both sides as they tackled broad legal questions raised in the case. Alito’s absence raises the possibility of a 4-4 split ruling that would leave the legal issues unresolved while allowing the Boulder case to move forward.

Boulder officials say they face increasing costs because of the impacts of climate change, including efforts to minimize risks from wildfires. Just this summer, Colorado has experienced extreme heat, drought and multiple fires.

The lawsuit, bringing claims under state law, says Exxon and Suncor misled consumers about the impact that greenhouse gases produced by their products would have on the climate.

The companies deny the allegations and warn that if the Boulder lawsuit and others like it are able to move forward to trial, they and other energy companies could face crippling damages in the billions of dollars. They also argue climate change is such an inherently national and international issue that it cannot be the subject of litigation in state courts.

There was some sympathy from the bench toward the oil companies and the potential for crippling damages.

Chief Justice John Roberts, one of the court’s conservatives, wondered how many more cities and counties would launch similar lawsuits if the court allows the Boulder case to continue.

“Just to make sure I have a correct understanding. Presumably, if you prevail, the next day a municipality in every single state will file a lawsuit,” he told Boulder’s lawyer.

Although Boulder’s claims are based on consumer deception, Roberts also seemed skeptical that the lawsuit was anything other than what he called “an effort to reduce emissions.”

On the other hand, Roberts, in an exchange with the oil companies’ lawyer earlier in the argument, said litigation brought in state court against out-of-state companies over an alleged harmful product is commonplace.

Other justices also seemed conflicted. Liberal Justice Elena Kagan at one point compared climate litigation with the wave of lawsuits against tobacco companies and drug manufacturers who sold opioids, which were allowed to proceed.

The oil companies have pushed back on such comparisons, saying that in the tobacco and opioid litigation there was a much more direct connection between the product and alleged harm to consumers.