The United States Postal Service announced Tuesday that it had temporarily stopped accepting packages from China and Hong Kong, hours after an order by President Trump took effect that ended duty-free handling of many smaller parcels.

Mr. Trump ordered on Saturday that all goods leaving China starting on Tuesday must follow the rules for higher-value shipments. Until the change, parcels worth up to $800 apiece were not required to include detailed information on their contents and were not subject to tariffs.

The United States imports close to four million of such lower-value parcels a day with little or no customs inspection and no duties collected — with most of them coming from China.

The Trump administration and other critics have contended that allowing these packages into the United States has created a conduit for fentanyl, a synthetic opioid, and related supplies to enter the United States.

But the duty-free provision on lower-value parcels, known as the de minimis rule, has also been used by many e-commerce companies to bring regular consumer items from China into the United States without paying tariffs on them.

FedEx and UPS are also affected by the change in customs rules, as they move a large portion of the parcels, running frequent cargo flights from China to the United States. Neither company has responded yet to questions about how they will handle the new rules.

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