Azief could spare six days to delay and increase his strength because he believes in six days the Demon King would not do anything excessive to Katarina.
Because Katarina is a bait.
Of course his calculation might be wrong.
If it's wrong and the Demon King did something that is unforgivable to Katarina. He would make sure the entire Seresian world would pay for it.
His choice then would be simple.
He just has to increase his strength on Earth and when he had enough strength he could go to the Seresian world and exact his revenge.
And if he could think of this, he believes that the Demon King could also thought of the same thing
And without a bait, Azief is free to do what he wants.
And that is something that the Demon King would not do.
But because of what happened to the portal, right now Azief is anxious.