[Greysard]

Putin only needs to point out that the USA offers the same right of asylum. Per Wikipedia:

The United States honors the right of asylum of individuals as specified by international and federal law. [...] Asylum eligibility has three basic requirements. First, an asylum applicant must establish that he or she fears persecution.[2] Second, the applicant must prove that he or she would be persecuted on account of one of five protected grounds: race, religion, nationality, political opinion, and social group. Third, an applicant must establish that the government is either involved in the persecution, or unable to control the conduct of private actors.

Snowden:

1. Fears persecution, and that has been already proven;
2. Is persecuted for his political opinion. Technically what he did is a crime, but many political refugees are charged with some crime by their governments - it's always illegal to oppose the dictator.
3. The US government is directly involved.

This is in accordance with UN agreements on human rights. Perhaps if the USA and Russia had a mutual agreement on extradition then things would be different. But then Russia would ask for extradition of many characters, shady or not.

[Little Pig]

The Russians can go on to add that the US has not sent back any of the many Russians currently residing in the US who have given the US the same kinds of “secrets” that Snowden holds.