What is the interaction between Empowered Spell and Booming Blade or Green-Flame Blade?

Can you reroll the damage dice that come as part of the melee weapon attack? That is, is the melee weapon attack part of the damage for the spell?

Empowered Spell reads:

When you roll damage for a spell, you can spend 1 sorcery point to reroll a number of the damage dice up to your Charisma modifier (minimum of one). You must use the new rolls.

Booming Blade and Green-Flame Blade read:

As part of the action used to cast this spell, you must make a melee attack with a weapon against one creature within the spell’s range, otherwise the spell fails.