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WASHINGTON — Google’s Motorola Mobility unit lost an appeals court bid to invalidate a Microsoft patent used to win a ban on U.S. imports on some mobile phones.

Motorola Mobility failed to prove the technology covered by Microsoft’s patent was previously used in Apple’s failed Newton personal digital assistant of the 1990s, the U.S. Court of Appeals for the Federal Circuit in Washington said in an opinion posted on its website Monday. Motorola Mobility conceded it infringed the patent, pinning its arguments on claims the invention wasn’t new.

The patent, which covers a way mobile devices synchronize calendars with computers, is part of Microsoft’s ActiveSync software that Motorola Mobility licensed before the two companies started fighting. Microsoft has also sued U.S. officials, claiming the import ban isn’t being enforced.

The case is part of a broader argument by Microsoft that Google’s market-dominant Android mobile phone operating system uses its technology. Motorola Mobility, which was acquired by Google in 2012, is one of the biggest holdouts from an Android licensing program that Microsoft started three years ago.

Google’s Android operating system is the most popular platform for smartphones, with 81 percent of the global market in the third quarter, according to data compiled by Bloomberg. Motorola Mobility’s handset sales don’t rank in the top 10. Microsoft’s operating system, used with Nokia’s Lumia phones, had 3.7 percent of the market.

Microsoft separately appealed aspects of the U.S. International Trade Commission case it lost. The Federal Circuit in October revived Microsoft’s claims involving one patent. Since the patent expires this month, Google wouldn’t face any import ban from the ITC though the ruling boosts Microsoft’s chance of seeking cash compensation in district court.

Microsoft contends any Motorola Mobility phone that has the syncing feature infringes the patent, and has sued U.S. Customs and Border Protection, saying its officials aren’t stopping phones from entering the U.S. The government has asked that the case be dismissed.

A Motorola Mobility case against Microsoft, seeking to block imports of the Xbox video-gaming system, failed at the ITC and is on appeal.