HONG KONG — Chanting slogans like “Shame, U.S. government,” demonstrators marched from a downtown park to the United States Consulate on Saturday to urge that Edward J. Snowden, the former National Security Agency contractor accused of leaking documents about American surveillance programs, be allowed to remain in Hong Kong.

One of the protest’s organizers, Tom Grundy, a British expatriate, called on China and the United States to refrain from pressuring Hong Kong about Mr. Snowden. “We want an independent judiciary to decide on the case,” Mr. Grundy said.

Hong Kong, which was ruled by Britain until its return to China in 1997, retains a legal system that is widely respected for its independence in its status as a special administrative region of China. Some activists, however, have criticized recent court appointees as having more pro-Beijing connections than their predecessors.

In his first comment on Mr. Snowden’s case, Hong Kong’s chief executive, Leung Chun-ying, indicated Saturday that Hong Kong would follow established procedures if it is asked to surrender Mr. Snowden to the United States. He also indicated that the Hong Kong government would look into Mr. Snowden’s disclosure that the National Security Agency might have gained covert access to the main hub of Internet servers here, located at the Chinese University of Hong Kong.