[Keeper of Dol Guldur]

I think, even should Morgoth be involved in the equation, Sauron was acting to take over the world and have everything ordered his way. He didn't worry about the Valar because once that was achieved maybe he hoped the Valar would see the genius in his control, and how well everything worked together. Honestly, after total control was achieved Sauron may have decided to wipe out the unorganized scum of the orcs entirely, now having men and dwarves, and all the other races as his well-ordered pawns.

Another possibility, is that the Valar while having dealt effectively with Morgoth, who was their peer and brother, and therefore their responsibility, felt unobliged to deal with Sauron. They felt it was the responsibility of the peoples of Middle-Earth to deal with Sauron, being then a plague on Middle-Earth and not directly confronting or challenging the might of Valinor. Of course, as a Maia, they compromised somewhat on responsibility for his actions, and sent the Istari, other Maia of Sauron's race, to counsel and advise in ways that would hinder his progress.