[Phone checks at Hong Kong’s border worry travelers to mainland China.]

The White House’s restraint on the issue has stood out in Washington, where the protests have been the source of a rare sight: broad bipartisan agreement.

Mitch McConnell, the Senate majority leader; Kevin McCarthy, the House minority leader; and Marco Rubio are among the Republicans who have put out full-throated statements in support of the protests. Across the aisle, Nancy Pelosi, the House majority leader; Chuck Schumer, the Senate minority leader; and most of the Democratic nominees for president have done the same.

The protesters, initially stirred in opposition to a proposed law that would allow extraditions to mainland China, have expanded their demands to include universal suffrage, an independent investigation of the police’s handling of the demonstrations, and amnesty for hundreds of arrested protesters. The protests have been mostly peaceful but have occasionally turned violent, including a chaotic scene at the airport Tuesday when demonstrators attacked two men from mainland China, including a journalist.

The police have routinely used tear gas, pepper spray and batons to disperse protesters. Hong Kong officials have resisted an independent commission of inquiry into police tactics, some of which have been condemned by international groups including the United Nations Human Rights office, Amnesty International and Human Rights Watch. The government asserts that an investigation already underway by a police watchdog is adequate, but critics say the body is staffed with pro-government figures.

Nor have officials indicated any willingness to submit to the protesters’ demands, increasing fears that the impasse could lead to a bloody, Tiananmen-style crackdown by Beijing. Mr. Trump tweeted on Tuesday that the Chinese government had moved troops to the border with Hong Kong, and encouraged everyone to be “calm and safe.”

A garrison of soldiers with the Chinese People’s Liberation Army is stationed in Hong Kong, but most observers consider it unlikely that Beijing would use it to squelch protests unless as a last resort, as it would all but destroy the territory’s autonomy and could have a devastating economic impact.

Two outspoken Hong Kong politicians who support the protests took their message to the United States on Thursday, placing responsibility for the crisis entirely on Carrie Lam, the chief executive of Hong Kong, and expressing deep concern about the possibility that Chinese forces could intervene to crush the movement.