WASHINGTON—The Trump administration is moving closer this week to levying tariffs on nearly half of Chinese imports despite broad opposition from U.S. business and the start of a fresh round of talks between the U.S. and China to settle the trade dispute.

The twin administration initiatives—pursuing tariffs on $200 billion of Chinese goods while relaunching talks to scrap tariffs—underscore a split within the U.S. administration, with negotiators in the U.S. Treasury Department offering a carrot, while the office of the U.S. trade representative threatens with a stick, both with the approval of President Trump, according to people familiar with the administration’s internal deliberations.

“Trump is a deal guy,” said one person closely following the talks. Until the Chinese make a concrete offer, the person said, Mr. Trump will continue to encourage the dueling agencies about what action to take.

President Trump, a Republican, continues to take a skeptical, hawkish view toward Beijing, said U.S. officials. At a fundraiser on Friday in the tony Hamptons section of New York’s Long Island, he focused on China, said two participants. The message was: “They better pay attention because we’re not done with those guys yet,” said one of the participants.

Monday was the first of six full days of public hearings on the next round of tariffs, where about 360 company and trade association officials are expected to testify on the impacts of the tariffs on their industries. As in past hearings on the China trade dispute, which involves U.S. claims that Chinese firms obtain U.S. intellectual property by theft or coercion, the participants generally requested exemptions from the tariffs because they felt the levies would hurt business prospects.