The source of the additional celebration on the fifteenth of Adar (Shushan Purim) is the respite from the additional battle in Shushan on this day. Chazal linked this day specifically to cities that have been walled from the time of Yehoshua bin Nun, which requires explanation, since Shushan itself was not walled then! The Talmud Yerushalmi writes that this is in order to give honor to Eretz Yisrael.

Rav Hutner explains that there are two kinds of war against Amalek: The first is when they come to attack us and we go out to fight them. The second is when we initiate war against them. In the times of Moshe, "Amalek came and battled Israel in Rephidim" (Shemot 17:8), whereas in the times of Shaul we attacked them, "Go and strike down Amalek." (Shmuel I 15:3)

The same was true in the times of Achashverosh. At first Haman attacked us, "He sought to destroy, to kill, and to annihilate," which was on 13 Adar. On the fourteenth we attacked them, "Let tomorrow also be given to the Jews who are in Shushan." (Esther 9:13)

Between these two types of wars there was a respite, "gaining relief from their foes." (9:16) This is what the Torah says, "It shall be that when Hashem, your G-d, gives you rest from all your enemies all around ... you shall wipe out the memory of Amalek." (Devarim 25:19) After the rest from the war that they initiate against us, we attack them.

This obligation to go out to war against Amalek is dependent, in time and place, on Eretz Yisrael. "Bnei Yisrael were commanded to perform three mitzvot when they entered the Land: To destroy the descendents of Amalek, etc." Therefore, the sanctity of the fifteenth day is linked to Yehoshua's conquest, since this conquest mandates the second phase of the war -- that we go and attack them, and this is the honor of Eretz Yisrael. Therefore, the day on which we commemorate our attack against them -- the fifteenth day, on which we rested in Shushan -- is linked to the honor of Eretz Yisrael and to the conquest of Yehoshua bin Nun, and therefore it is practiced in places that are walled from the times of Yehoshua.

This war has a special connection to Yerushalayim, since Moshe says to Yehoshua, "Tomorrow I will stand on the top of the hill." This is the known hill. Rav Nebenzahl shlita writes, based on the Midrash, that Har Moriah accompanied Israel in their travels through the desert, as it says, "to the mountain of the Mor." (Shir Hashirim 4:6) This is what it says, "For the hand is on the throne of G-d." The Name is not complete nor is the throne complete until the descendents of Amalek will be destroyed, and this will be in the end of days: "At that time, people will call Yerushalayim, "The Throne of Hashem.'" (Yirmiya 3:17)

It is amazing to note that the gematriya of "rosh hagiv'ah" (top of the hill) is 586, just as that of "Yerushaleim." Rav Nebenzahl further notes in the name of his rebbe, the Rosh Hayeshiva of Mir, Rav Nachum Partzovitz zt"l, that Bnei Yisrael reached the Desert of Zin on 15 Iyar. The next day, on Sunday, the manna first fell, and on Friday they collected a double portion. Afterwards they traveled to Rephidim and camped there, so that Sunday was 23 Iyar. On Friday they fought with Amalek, and then Moshe held back held the sun, so as not to violate Shabbat. According to this calculation, the battle against Amalek took place on Friday, 28 Iyar. Thus, a war took place at the footsteps of the hill, Har Hamoriah of Yerushalayim, on the 28th of Iyar (which is the day of the Liberation of the Old City in '67). This is not mere coincidence!