# ListDensityPlot interpolation only in one direction

I am using ListDensityPlot to plot a set of graphs, i.e. I have got a rectangular grid. Is there any way how to prevent interpolation along the y axis and interpolate data only in the x direction? So far I was thinking only about "pre-interpolation" of my dataset before I plot it and then using InterpolationOrder->0.

data = Table[Sin[x y], {x, 0, 3, 1.}, {y, 0, 3, 1.}];