It looks like it could be some type of slate tile.

I had the same problem when I remodeled my kitchen, laundry room and bathrooms. I only needed fill-in tile next to walls and cabinets. It was matter of taking a tile to every tile store and outlet in two cities to find something that blended. It worked out really well, you can't see a difference. If you need tile for a large area in the middle of a room, it might be a dicier situation. Good luck!

Sometimes you can "steal" some original tile from a closet or pantry. It rather depends on the subfloor and the ability of the tile guy.