The United States said Sunday it was "disappointed" by Hong Kong's "troubling" failure to arrest Snowden before he fled the territory.
Snowden, who embarrassed US President Barack Obama with his revelations of massive surveillance programmes, dramatically flew from Hong Kong bound for Moscow, despite Washington having requested his arrest and extradition.
The ex-CIA technician was holed up in the southern Chinese city where he issued a series of leaks on the NSA gathering phone call logs and Internet data since May 20, until his departure on Sunday.
"I can tell you in no uncertain term that we have not been deliberately delaying the progress, all along, we act fully in accordance to the law," Yuen said.
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He said that the US request for Hong Kong to produce a provisional arrest warrant was received on June 15, where the US charged Snowden of with espionage, theft and conversion of government property.
Yuen said he told US Attorney General Eric Holder on June 20 that the issue of Snowden was complicated and that Department of Justice staff needed time to handle it.
Yuen also said there were discrepencies and missing information in documents used to identify Snowden.
"On the diplomatic documents, James was used as the middle name, on the record upon entering the border, Joseph was used as the middle name, on the American court documents sent to us by the American Justice department, it only said Edward J Snowden," he said.
Yuen said the US had not responded to the Department of Justice's questions up to the point of Snowden's departure from Hong Kong on Sunday.