On a very low calorie diet
the metabolism will most likely slow down unless you're getting most of your calories from protein
or very complex carbohydrates.
In general weight-loss causes the metabolism to go down because the body has to run a smaller weight. If you're trying to increase your metabolism go on a little car ketogenic diet for most of your calories come from lean protein and some bastable's and a little bit of fruits as well as healthy fats like planned or fish-based fat.