You could use something like Mapei Renovation screed (slc) to bring the floor up 3mm but I think that's the limit for it ie you can't lay it thinner.
If it's only a difference of 3mm between the two floor heights I would just use a thicker adhesive bed to lay the tiles on, assuming the existing tiles are not on a ridiculously thick bed.
It's time for some calculations to be done. You will need to know the thickness of the new tiles, the trowel you plan to use and then you can work out how much to raise the floor level by e.g if your new tiles are 10mm thick and you plan to use a 1/2 inch square notch trowel (which gives around a 6mm bed depth) you need to raise the floor level to around 16mm below the top of the existing tiles.