BEIJING—China acknowledged it has demographic challenges, saying its population will peak in 2030 but left little hope the country would further ease birth restrictions after lifting its one-child policy a year ago.

The country’s State Council, its cabinet, unveiled a key plan detailing deep demographic changes over the next 15 years, including low birthrates and a rapidly aging population, but said it would stick to a policy of letting families have a maximum of two children.

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