WASHINGTON—The Senate unanimously passed legislation that would re-examine U.S. support for the Hong Kong government as clashes between police and protesters seeking to counter Beijing’s control over the largely self-governing territory grow more violent.

Mass protests in Hong Kong began months ago in reaction to a now-withdrawn bill that would have allowed suspects to be extradited to China. The demonstrations have since become a broader movement opposing the government of the historically semiautonomous city, where Beijing has resisted calls to expand democratic freedoms. Some protesters have appealed directly to U.S. lawmakers for support, traveling to Washington to meet with members of Congress, including House Speaker Nancy Pelosi (D., Calif.).

The Senate bill, approved through a unanimous consent vote, would require the U.S. secretary of state to certify annually that Hong Kong remained sufficiently independent from Beijing to warrant the special status that has helped the city grow into a global financial hub. It would also task the president with placing sanctions on individuals who have suppressed human rights in Hong Kong.

Those measures largely reflect the components of a bill that passed the House last month, though the two pieces of legislation aren’t identical. The Senate version, for example, enforces sanctions in fewer circumstances.

The Senate also unanimously passed legislation barring the U.S. sale of certain munitions, including tear gas and pepper spray, to the Hong Kong Police Force. The House has passed similar legislation.