It is the first trial to resume after the end of year festive holidays.
During 1994 genocide, the priest, who has pleaded not guilty, was vice-chancellor of the College of Christ the King of Nyanza, southern Rwanda, one of the most prestigious schools of the country.
The prosecution Monday called a witness who worked at the College of Christ the King and claimed that the accused had ordered death of a Tutsi identified as Kayombya, who lived in the vicinity of the College.
Presenting himself as "an old man who can neither read nor write", the witness alleged that the victim was never seen again.
"I never saw him again (...) I concluded that they killed him", he told the court, without elaborating further.
Nsengimana was arrested in March 2002 in Yaounde, Cameroon, and was transferred to the ICTR detention facility in April, the same year.
The accused is among other three Rwandan catholic priests indicted before the UN court over their roles in the 1994 killings.
Hirondelle News Agency