Substituting one ingredient for another in a recipe is not always as simple as making a straight substitution. While tomato puree and diced tomatoes are obviously both made from the same basic ingredient, they add completely different flavors and consistencies to a dish. Diced tomatoes can work well as a garnish or finishing touch. Tomato puree is generally more incorporated into the recipe, providing extra thickness and a smooth texture. With that said, however, you can successfully substitute tomato puree for diced tomatoes in some recipes.
Assess the dish carefully to determine whether it can hold up with tomato puree rather than diced tomatoes. If you are making a fairly wet, liquid dish -- such as a stew, chili or soup -- chances are you can substitute tomato puree for diced tomatoes successfully, though the texture and flavor of the final dish will probably be noticeably different. If your recipe relies on the texture of the diced tomatoes, however -- such as in the case of salsa -- you should not make the substitution.
Measure out an amount of tomato puree equal to the amount of diced tomatoes required in the recipe you are making.
Add the tomato puree to the recipe well before you would have added the diced tomatoes. The tomato puree can handle long cooking times much better than diced tomatoes, which would crumble and disintegrate. Cooking the puree for longer will help incorporate its flavor into the rest of the recipe.