Leung broke his long silence on the affair to amplify a government statement issued yesterday when Snowden dramatically flew out of Hong Kong, escaping a US arrest warrant.
The city government's chief executive noted "expressions of displeasure" from some in the United States, but told reporters that "the people of Hong Kong expect Hong Kong to uphold its own laws including the Basic Law".
The Basic Law is capitalist Hong Kong's mini-constitution guiding its "one country, two systems" form of autonomy under the rule of communist China.
But he said: "Under the one country, two systems, of course we surely need to communicate with the central government and discuss events that are related to foreign affairs."
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Snowden, a former contractor at the National Security Agency, is wanted by the United States on theft and espionage charges after he fled to Hong Kong in late May and began leaking details of NSA programmes.
That decision provoked fury in Washington and Leung said he "understood" US complaints against Hong Kong. But the city had not received any notification that Snowden's passport had been voided by the US State Department, he said.
Some lawmakers in the Chinese territory are concerned at the possibility of US reprisals, such as a withdrawal of visa-free access to the United States for Hong Kongers.
"I personally treasure relations between Hong Kong and the United States on various aspects," he stressed.
"I believe our friends in the United States, including government officials and in the business sector, treasure their relations with Hong Kong."
Leung recently went on a trade-promotion trip to New York, where he repeatedly refused to answer questions about Snowden during an interview with Bloomberg TV on June 12.