A direct fuel injection engine basically comprises a combustion chamber, a piston with a cavity, a fuel injection valve, a spark plug and a control unit. The fuel injection valve is configured and arranged to directly inject a fuel stream into the combustion chamber in a substantially constant hollow circular cone shape in a stratified combustion region. The control unit is configured to ignite a first air-fuel mixture formed directly after the fuel stream is injected and prior to a majority of the fuel stream striking the cavity when the direct fuel injection engine is operating in a low-load stratified combustion region, and to ignite a second air-fuel mixture formed after a majority of the fuel stream is guided by the cavity toward an upper portion of the combustion chamber above the cavity when the direct fuel injection engine is operating in a high-load stratified combustion region.