The present invention is directed to a dual fuel supply system for supplying fuel to a direct-injection system of a diesel engine. The dual fuel supply system includes a diesel supply system to supply diesel to the direct-injection system; and a mixed fuel supply system that is operatively able to supply a liquid fuel premixture of diesel and liquefied gaseous fuel to the direct-injection system at a supply pressure within a fuel demand pressure range of the direct-injection system and at a corresponding temperature range that retains the fuel premixture below its vapor temperature as it flows through the fuel path of the direct-injection system and the diesel engine. The dual fuel supply system is configured to permit selective change over between the diesel supply system and the mixed fuel system to supply the direct-injection system selectively with either diesel or liquid fuel premixture respectively.