A subject-matter of the present invention is a dyeing composition comprising, in an appropriate medium, at least one dye precursor, and at least one water-soluble or water-dispersible amphiphilic block copolymer comprising at least one hydrophilic block and at least one hydrophobic block without a fatty chain of more than 8 carbon atoms, the hydrophilic block or blocks representing at least 30% by weight of the block copolymer, with the exception of block copolymers of ethylene oxide and of propylene oxide, block copolymers comprising urethane units and block copolymers comprising siloxane units. The composition of the present invention makes it possible in particular to obtain an intense colouring of the keratinous fibres while retaining a soft feel and ready disentangling subsequent to the colouring.