PARIS — French antiterrorism prosecutors on Friday took over the investigation into the killing of four people the day before at Paris Police Headquarters, suggesting investigators were considering a possible terrorism motive.

The exact reasons for the opening of a terrorism inquiry were unclear, but it was likely to raise questions about whether the attacker — who worked in the Paris police intelligence unit, a highly sensitive department — had been sufficiently vetted.

Prosecutors in Paris said only that “elements gathered at this stage by investigators” had led them to hand the case over to the national antiterrorism prosecutor’s office.

They did not say whether an interview with the suspect’s wife or analysis of his cellphone and computer had guided their decision. A spokesman for the antiterrorism prosecutor’s office could not be reached to comment.