A three-judge panel will decide if President Trump’s tariffs are constitutional after hearing two hours of arguments Tuesday. The case — the first major legal test of the tariffs — is being decided by the little-known United States Court of International Trade, which has jurisdiction over tariffs and trade in the United States.

A libertarian public-interest litigation firm, the Liberty Justice Center, is representing a New York wine and spirits importer, V.O.S. Selections, and several other small businesses that say the tariffs are causing them irreparable harm. The suit claims Mr. Trump doesn’t have the authority to impose the tariffs.

The president unveiled the tariffs on his “Liberation Day” in April. He used the Nixon-era International Emergency Economic Powers Act to declare a national emergency and levy a 10 percent tariff worldwide on imports. Other countries, including China, were punished with much higher tariffs.

The plaintiffs claim that, under the emergency powers act, the president may invoke those powers only after declaring a national emergency in response to an “unusual and extraordinary threat” to national security, foreign policy, or the American economy originating outside of the country. They say the trade deficit does not meet that threshold and Mr. Trump’s almost immediate 90-day pause in applying the tariffs showed that it is not an emergency.

The center’s senior counsel, Jeffery Schwab, also told the judges that the IEEPA doesn’t allow tariffs and Mr. Trump’s tariffs are “unprecedented and unlawful.”

“This case is so far outside what an emergency is,” Mr. Schwab argued.

The Trump administration argued in court that the trade deficit has increased 40 percent in the past five years and threatens the nation’s supply chain and defense industry. The deputy assistant attorney general arguing the case said the cumulative effects of that trade imbalance created the emergency.

“I think that is a big problem,” the Department of Justice’s Eric Hamilton told the judges, adding that the national emergency declaration is a political question and not a legal question. “This is a relatively simple case,” Mr. Hamilton said.

The plaintiffs are asking for either a preliminary injunction to temporarily block the tariffs or for the judges to issue a summary judgement to block the tariffs outright. The administration’s lawyers want the lawsuit thrown out and claim the plaintiffs have not shown harm from the tariffs.

The judges did not indicate at the end of the arguments when they would decide the case. Any ruling they make can be appealed all the way up to the Supreme Court.

The Liberty Justice Center’s lawsuit is one of seven court challenges to Mr. Trump’s tariff policies, and it is the first to seek a ruling that would stop the tariffs from moving forward.