WASHINGTON—President Trump suggested a “personal meeting” with China’s President Xi Jinping to discuss the escalating crisis in Hong Kong and warned China it must respond “humanely” to the protests if it wants to strike a trade deal.

Mr. Trump’s statement via Twitter marked a shift in tone in his public statements regarding the situation in Hong Kong and for the first time linked the administration’s fragile trade talks with Beijing to the protests. The Wednesday evening tweets came amid growing concern within the administration...