HONG KONG — China granted initial approval for 16 new trademarks to Ivanka Trump, the president’s elder daughter and senior adviser, renewing questions about the Trump family’s intermingling of official roles and international business interests.

Among the broad array of trademarked items were shoes, shirts and sunglasses — the sort of products that were sold under her recently closed fashion label. Other categories given initial approval were less obvious fits, like voting machines, homes for senior citizens and semiconductors.

Representatives of Ms. Trump and the Trump Organization have previously described their trademark applications in China as part of a global effort to protect their names in places where intellectual property rights infringement is rampant.

But that effort has spurred criticism that the Trumps’ roles in government smooth the way for the trademark approvals, and that the prospect of future Trump business in China clashes with the White House’s attempts to challenge the country over trade.