The U.S. statements came after Hong Kong police shot and critically wounded a protester and a man was set on fire in violence that prompted leader Carrie Lam to denounce the demonstrators as "enemies of the people."
Xi met Lam on the sidelines of a trade event in Shanghai on Monday night amid signals from China's central government that it may tighten its grip on Hong Kong to quell the unrest that has at times challenged Chinese rule.
Police deployed at least two water cannon trucks in the vicinity. They had issued warnings to protesters who occupied the area that they were taking part in an unauthorized rally and were violating a government ban on face masks.
One of the measures, the Hong Kong Human Rights and Democracy Act, would require the US secretary of state to certify every year that Hong Kong retained its autonomy in order to keep receiving the special treatment that has allowed it to be a major financial center.
Hong Kong protests: Today's attack on Ho marked a dark turn in the protests that began in early June, and demonstrators have accused police of being slow to respond or even colluding with the attackers.
The mask ban, which took effect Saturday under an emergency law, has led to more anger instead of deterring the anti-government demonstrations that have rocked the international financial hub for four months.