Does the attack granted by the Vampiric Touch spell allow me to make a bonus-action weapon attack with Two-Weapon Fighting?

Question

Once I have cast vampiric touch I can make a melee spell attack "on each of [my] turns as an action".

In the first round, the round I cast the spell my action is to 'Cast a Spell', and I clearly can not use Two-Weapon Fighting. However, in subsequent rounds my action is to make an attack. Does this attack allow me to use the Two-Weapon Fighting rule and make an attack with a light weapon in my off hand as a bonus action?

Two-weapon fighting stipulates that you must make an attack with a weapon. So the crux of the question:

Is a melee spell attack with vampiric touch equivalent to attacking with a weapon for the purposes of using Two-Weapon Fighting?

I would consider a hand that can do 3d6 necrotic damage a weapon.

Answer 1

RAW, the answer is negative.

Two-Weapon Fighting: When you take the Attack action and attack with a light melee weapon that you’re holding in one hand, you can use a bonus action to attack with a different light melee weapon that you’re holding in the other hand. You don’t add your ability modifier to the damage of the bonus attack, unless that modifier is negative. (PHB, p. 195)

(emphasis mine)

So, you would have to make an attack with the weapon held on the main hand first, to actually have available a bonus action to attack with your off-hand. Vampiric Touch is a melee spell attack that has nothing to do with weapon combat (it does not even require you to have an empty hand to cast it repeatedly), so it does not qualify either as a wielded light weapon or melee weapon attack.

Related: What is the difference between a "ranged attack" and a "ranged weapon attack"?