A low-emissions high-pressure multi-fuel burner includes a fuel inlet, for receiving a fuel, an oxidizer inlet, for receiving an oxidizer gas, an injector plate, having a plurality of nozzles that are aligned with premix face of the injector plate, the plurality of nozzles in communication with the fuel and oxidizer inlets and each nozzle providing flow for one of the fuel and the oxidizer gas and an impingement-cooled face, parallel to the premix face of the injector plate and forming a micro-premix chamber between the impingement-cooled face and the in injector face. The fuel and the oxidizer gas are mixed in the micro-premix chamber through impingement-enhanced mixing of flows of the fuel and the oxidizer gas. The burner can be used for low-emissions fuel-lean fully-premixed, or fuel-rich fully-premixed hydrogen-air combustion, or for combustion with other gases such as methane or other hydrocarbons, or even liquid fuels
