Take out the wooden threshold in between the door jambs and do one of two things:
1.) Make or have made a wider wooden threshold that matches the width of the door jamb.
2.) Get a marble threshold that is the width of the jamb, usually 4 1/2", cut to length and install in place of the wood threshold. The marble will normally be 3/4" thick, so get one with beveled edges. The bottom of the bevel will be at aprox. 1/2" up from the bottom edge. It makes for a nice transition to the wood and the tile.
3.) Either way will end up with a very slight gap between the tile and threshold, aprox. 1/8". I would get a tube of caulk from the tile shop that matches your grout and caulk the gap.
Mike Hawkins