Which nazi federal agency was responsible for hunting Jews during ww2?

The Schutzstaffel, more commonly referred to in English as the SS. Within the SS, it was the Einsatzgruppen that was specifically in charge of hunting and killing the Intelligentsia (i.e., Jews, Soviet political commissars, Gypsies, and actual or alleged partisans throughout Eastern Europe). Also, the SS was divided into three subdivisions: Allgemeine SS (General SS) and Waffen-SS (Armed SS) and SS-Totenkopfverbände (Concentration Camp Administrators and Guards). The Allgemeine SS was responsible for enforcing the racial policy of Nazi Germany and general policing, so if by "hunting," you mean finding, then they were part of it. The Waffen-SS consisted of combat units within Nazi Germany's military, so if by "hunting" you mean it in a conventional sense of being armed and hunting an animal, then they were part of it. The SS-Totenkopfverbände (SS-TV) ran the concentration camps and oversaw extermination, so if by "hunting" you are including any and all killing then they were part of it. Additional subdivisions of the SS included the Gestapo and the Sicherheitsdienst (SD) organizations, which was tasked with the detection of actual or potential enemies of the Nazi state, the neutralization of any opposition, policing the German people for their commitment to Nazi ideology (including the hunting of Jews, purification of the German race, and implementation of the Final Solution), and providing domestic and foreign intelligence.

Any student of history will tell you that Nazi Germany's organizational structure, despite all the preaching about "order," was anything but well-ordered. It was actually quite chaotic with various agencies and groups having overlapping authorities that led to a considerable amount of confusion about who was actually in charge of what, quite heated turf wars within the Nazi hierarchy over authority, and politicking that at times was quite literally cutthroat. Some suggest that this may have been on purpose with Hitler encouraging the competition and letting authority go to those who successfully seized it from others, but if by design, Nazi Germany's organizational chart would not look so haphazard and ad hoc, exhibiting some level of planning and design instead of unplanned and made up as Hitler went along. So saying that any one agency or group was in charge of hunting Jews is simply not a historical reality.

The Gestapo.

It was a coordinated effort between the SS and every other agency. It was government policy therefore ALL German government agencies had blood on their hands, right down to the Deutsche Reichsbahn which ran the train which carried the Jews to the gas chambers. See the movie "Conspiracy" with Kenneth Branagh and Stanley Tucci

Reichssicherheitshauptamt oder RSHA

The Gestapo and SS.

The Reich Main Security Office which controlled the Security Police and the SS. It reported directly to Himmler

The Waffen-SS