The Nintendo Switch booth at the China Digital Entertainment Expo and Conference in Shanghai in August. Photo: staff/Reuters

OSAKA, Japan— Nintendo Co. NTDOY -0.39% reported strong sales of its new Switch Lite hand-held game machine, auguring well for the holiday season.

The Kyoto-based company said Thursday it sold 1.95 million units of the Switch Lite, released on Sept. 20, and 2.85 million units of the original Switch during the July-September quarter. The $200 Switch Lite is a cheaper alternative to the original $300 handheld-hybrid Switch console introduced in March 2017.

Analysts said the Lite’s sales beat expectations in the U.S., traditionally a tough market for hand-held game machines. Nintendo said it sold 800,000 units of the device in the U.S., more than twice as many as the 390,000 units it sold in Japan, where hand-held machines tend to be more popular.

“Selling 1.95 million units of the Switch Lite in 10 days is a great success, and I believe the first proof that the device is going to be a super hit in the long run,” Tokyo-based industry consultant Serkan Toto said.

Nintendo Chief Executive Shuntaro Furukawa said the Lite was drawing both existing Switch owners who wanted a second or third device for the family and new users who didn’t want to pay $300 for a regular Switch.

To attract more hand-held fans, the company plans to release games for the Switch platform that previously were available mainly for the older 3DS hand-held device, beginning with the launch of new entries from the Pokémon franchise next month. Ace Research Institute analyst Hideki Yasuda said the Pokémon games will likely further boost the Lite’s sales momentum.

Investors are also watching Nintendo’s plan to sell Switch consoles in China with Tencent Holdings Ltd. and the performance of Mario Kart Tour, a smartphone game that the company introduced on Sept. 25. Nintendo said initial interest in Mario Kart Tour was strong.

The company said its July-September net profit rose 34% from a year earlier to ¥45 billion ($414 million), beating analyst expectations, on ¥272 billion in revenue, up 23%. It kept its full fiscal-year net profit forecast unchanged at ¥180 billion pending results from the holiday season, which could prompt revisions.

Write to Takashi Mochizuki at takashi.mochizuki@wsj.com

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