WASHINGTON—The new U.S. special representative for Iran said Thursday the Trump administration is prepared to impose sanctions on all countries that buy oil from Iran after a deadline in November, including China, the top importer of Iranian crude.

Brian Hook, who has been appointed as special representative and chief of a new Iran Action Group at the State Department, said the U.S. would issue waivers from sanctions to countries that have made efforts to reduce their Iranian oil purchases.

India and South Korea are among Iran’s top oil customers. Both countries already have started to scale back imports and are hoping to obtain waivers to buy more time to replace Iranian crude.

But China repeatedly has said it has no plans to comply with a wave of U.S. sanctions that are due to be reimposed on Iran’s energy sector on Nov. 4. Some oil analysts expect China to increase Iranian imports instead, potentially undermining U.S. efforts to isolate Iran.

In a response to a question about China’s plan to continue importing Iranian oil at a State Department briefing on Thursday, Mr. Hook refused to rule out imposing secondary sanctions on Beijing as punishment.