In his commentary, R’ Meir Zlotowitz explains that Achashverosh gave permission to override, but not annul the previous decree. This was a dilemma for Mordechai and Esther to make Haman’s decree powerless without challenging its authority.
The Vilna Gaon and the Malbim wrote that Mordechai’s decree could only affect the vague, public copy of the original decree. It could not change the explicit, private memo that each governor received.
The Malbim adds that Achashverosh’s plan was for the second document to only clarify the first, vague decree.
The Ibn Ezra notes that Achashverosh could have come up with excuses for first document, like saying that the first document was the result of language confusion because Haman changed the wording of the original draft of the decree from “Jews can kill” to “Jews can be killed.”
Similarly, the Alshich writes that Achashverosh was saying that Haman left out a comma when he said (Esther 3:13) “l’abeid es kolHaYehudim” (“to kill all of the Yehudim”). A comma placed after kol could make the phrase appear as “to kill all, (by whom?) the Yehudim!”