The State of Mississippi has denied requests for DNA testing of evidence made by a prisoner set to be executed on Tuesday, potentially setting up what experts said would be a rare case in recent years in which a person is put to death with such requests unmet.

The Mississippi Supreme Court, in a 5-to-4 decision, ruled in April that the existing evidence tying Willie Jerome Manning to the murder of two college students in 1992 was so strong that the findings of DNA tests would not make a difference.

Lawyers for Mr. Manning say that there are flaws in the prosecution’s case, which is almost entirely circumstantial, but that at the very least tests of the available physical evidence should be conducted before his execution. They are now lobbying the governor.

Richard C. Dieter, the executive director of the Death Penalty Information Center, said that fights over testing were not uncommon but that if testing were not eventually allowed before the execution, “that would be very rare indeed.”