WASHINGTON, March 5 — A US trade court judge on Wednesday ordered the government to begin paying potentially billions of dollars in refunds to importers who paid tariffs that the Supreme Court said last month were collected illegally.

Judge Richard Eaton of the US Court of International Trade in Manhattan ordered the government to finalize the cost of bringing millions of shipments into the US without assessing a tariff, according to a court filing. He ordered the refunds to be made with interest.