WASHINGTON (Reuters) -- The United States is gravely concerned about deepening political unrest and violence in Hong Kong, Secretary of State Mike Pompeo said on Monday, urging the city's government to address public concerns and China to honor its promises of liberties.

In the U.S. Senate, the Republican majority leader, Mitch McConnell, said he hoped a way could be found to pass a bill that would place Hong Kong's privileged status in U.S. law under tighter scrutiny. He urged President Donald Trump to speak out on Hong Kong and not focus solely on efforts to secure a trade deal with China.

Pompeo told reporters the Chinese Communist Party must honor its promises to the people of Hong Kong and said the city's government bore primary responsibility for bringing calm back to Hong Kong.

"Unrest and violence cannot be resolved by law enforcement efforts alone. The government must take clear steps to address public concern," Pompeo said, while calling for an independent investigation into protest-related incidents.

In a significant escalation, Hong Kong police laid siege to a university in the city on Monday, firing rubber bullets and tear gas to push back anti-government protesters armed with petrol bombs and other weapons in an attempt to stop them from fleeing.

Demonstrators are angry at what they see as Chinese meddling in Hong Kong's promised freedoms after the then British colony returned to Chinese rule in 1997. They say they are responding to excessive use of force by police.

Beijing denies interfering in Hong Kong's affairs and has blamed Western countries for stirring up unrest, which poses the gravest popular challenge to Chinese President Xi Jinping since he came to power in 2012.

While criticizing China and urging administration action, McConnell has been accused by some critics of holding up legislation that would require regular certification that China was allowing Hong Kong to retain its autonomy.

He told the Senate he had worked to add language related to rights in Hong Kong in a spending bill that has been delayed by Democrats, who have refused to vote for legislation that provides funding for Trump's U.S.-Mexico border wall.

McConnell said the United States did not need to wait for new laws to act on Hong Kong.

"There are already significant tools at the administration’s disposal and I strongly encourage them to use them," he said.

"I would encourage this president, who has seen Chinese behavior for what it is with a clarity that others have lacked, not to shy away from speaking out on Hong Kong himself," McConnell said. "The world should hear from him directly that the United States stands with these brave men and women."

“So rather than focusing solely on trade, I encourage the administration to make Hong Kong’s autonomy a key topic within our bilateral diplomacy," McConnell added, saying it should use existing legislation to target those responsible for human rights abuses.

Trump prompted questions about his commitment to protecting freedoms in Hong Kong when he referred in August to its mass street protests as "riots" that were a matter for China to deal with.

He has since called on China to handle the issue humanely, while warning that if anything bad happened in Hong Kong, it could be bad for talks to end a trade war between the world's two largest economies.