Gay rights campaigner was arrested after the president's visit
He made the demand when he appeared in court on a charge of assault in connection with his attempt to "arrest" President Mugabe last month.
Mr Tatchell, 47, is accused of assaulting a policeman in Buckingham Gates, central London, on 30 October, during his protest against laws on homosexuality in Zimbabwe.
During the 10-minute early administrative hearing at Horseferry Road Magistrates Court, central London, Mr Tatchell said the CPS should consider the evidence he had handed police of alleged human rights abuses by President Mugabe.
'Duty to investigate'
"Under the 1984 United Nations Convention they have a duty to investigate," Mr Tatchell said.
Two other men, Chris Morris, 20 and Alistair Williams, 31, also appeared in court charged with public order offences which allegedly took place during the same incident.
All three pleaded not guilty and were released on unconditional bail.
Clerk to the Justices Gaynor Houghton-Jones ordered the men to appear before the court again on 26 November.
The hearing was taken by the clerk, in the absence of a magistrate, under the terms of the Justices Clerks Rules 1999, which came into effect on 1 November.
A spokesman for the Lord Chancellor's Department said the new rules extended the quasi-judicial powers of magistrates' clerks.