הלכה אויף ישעיהו 66:1

When Rosh Chodesh occurs on Shabbos, the haftarah Hashamayim Kis'i is read [The heavens are My throne].¹¹Isaiah 66: 1. If, by mistake, the haftarah of the weekly sidrah was read, [if the reader becomes aware of it] before he said the concluding berachos, he should also read Hashamayim kis'i and then say the berachos. If he only became aware of it after saying the berachos, he should say Hashamayim kis'i, without the berachos. If Rosh Chodesh occurs on a Sunday, the haftarah, Machar chodesh is read [Tomorrow is the new moon].¹²I Samuel 20: 18–42. If [the reader] made an error, the same halachah applies as that of Shabbos Rosh Chodesh. If Rosh Chodesh occurs on Shabbos and Sunday, the haftarah Hashamayim kis'i is read.

Beginning with the Shabbos following Tishah beAv and after that, for the next seven Shabbosos we read the haftoras "sheva denechamasa" [seven haftoras of consolation]. If the first day of Rosh Chodesh Elul occurs on Shabbos, the haftorah, Aniyah so'arah, is set aside ["O you afflicted, floundering in the storm,"] (Isaiah 54:11) and we read instead, "Hashamayim kis'i," [The heaven is My throne] (Isaiah 66:1), because this haftorah also contains consolation for Jerusalem. On the Shabbos of Parshas Ki Seitzei, when the haftorah Roni akarah [Sing, O barren woman] (Isaiah 54:1) is read, we conclude the haftorah with Aniyah so'arah, which is next to it. If, by mistake, on Shabbos Rosh Chodesh Elul, you said Aniyah so'arah, and you became aware of it before saying the concluding berachos, you should also say Hashamayim kis'i, and then say the concluding berachah. If you only became aware [of your error] after saying the concluding berachos, then you should recite, Hashamayim kis'i without the berachos. If Rosh Chodesh Elul occurs on Sunday, the haftorah, Machar Chodesh is set aside, [Tomorrow is Rosh Chodesh] (I Samuel 20:18), because it contains no consolation for Jerusalem, and the haftorah Aniyah so'arah is read.