WASHINGTON (Reuters) - President Donald Trump’s trade fight with China moved inside the white marble walls of the U.S. Supreme Court on Tuesday, where lawyers for both countries faced off over whether Chinese companies can be held liable for violating U.S. antitrust laws.

The White House is seen as the sun sets in Washington, U.S., February 7, 2017. REUTERS/Jim Bourg

The nine justices heard arguments in an appeal by two American companies of a lower court ruling that threw out price-fixing claims against two Chinese vitamin C manufacturers based on submissions by China’s government explaining that nation’s regulations. Many of the justices signaled skepticism toward that ruling.

The arguments gave both countries a chance to air their differences over an aspect of their trade relationship. The Supreme Court took the unusual step of letting China present arguments even though it is not an official party in the case. Typically, only the U.S. government is given that privilege.

The world’s two economic superpowers are engaged in an escalating trade fight. The United States, accusing China of unfair trade practices and theft of intellectual property, has threatened to impose tariffs on up to $150 billion of Chinese imports. China has threatened comparable retaliation against U.S. exports.

None of the heated rhetoric over tariffs trickled into Tuesday’s arguments, which remained respectful. The lawyer representing China, Carter Phillips, urged the justices to defer to China’s explanation about Chinese regulations. A U.S. Justice Department lawyer, Brian Fletcher, said such deference comes with limits.

The weight U.S. judges should give legal views expressed by foreign governments in their courts is pivotal to determining whether Chinese companies can escape liability for anticompetitive conduct mandated by China’s government.

The case began in 2005 when U.S. vitamin C purchasers Animal Science Products Inc, based in Texas, and The Ranis Co Inc, based in New Jersey, accused Chinese manufacturers including Hebei Welcome Pharmaceutical and North China Pharmaceutical Group of antitrust violations.

China intervened in the case, asking the trial court to dismiss the allegations in part because its laws had forced Chinese companies to comply with government-mandated pricing regimes. A federal judge questioned the credibility of the Chinese submissions and, after a 2013 jury trial, awarded the two U.S. companies $147.8 million in damages.

The New York-based 2nd U.S. Circuit Court of Appeals overturned the judgment in 2016, saying that when a foreign government directly participates in a case American courts are obligated to defer to that country’s characterization of its own laws.

During the Supreme Court argument, Fletcher called that 2016 ruling “too rigid” and said deference should be decided on a case-by-case basis.

Phillips said China has been clear and consistent in its submissions and its views deserve respect. Any assertion that China tried to improperly shield Chinese companies from U.S. law was “the opposite of respect,” Phillips added.

This was the first time China intervened in a U.S. court to present its views as a non-party in a legal dispute.