It is customary for the Kohanim to recite Birkat Kohanim at Minha on Tisha B’Ab and at Ne’ila on Yom Kippur. It occasionally happens that the prayer is scheduled late in the afternoon close to sunset, such that the Hazan will not reach Birkat Kohanim until after sunset, unless he rushes through the prayer service. Indeed, some Hazanim find themselves rushing through the Ne’ila prayer on Yom Kippur in order to ensure that Birkat Kohanim will be recited before the sun goes down. Is this necessary, or is it permissible to recite Birkat Kohanim even after sunset?
Hacham Ovadia Yosef addresses this question in his work Yehaveh Da’at (6:40), where he notes the debate among the Halachic authorities as to whether Birkat Kohanim may be recited at night. According to some opinions, the blessing cannot be recited during the nighttime hours. In deference to this view, Hacham Ovadia rules that Birkat Kohanim should not be recited after Set Ha’kochavim (nightfall), which occurs approximately 20 minutes after sunset. However, during the period of Ben Ha’shemashot, which extends for approximately 13-15 minutes after sundown, the blessing may be recited. Hacham Ovadia explains that during this period, we may apply the rule of "Sefek Sefeka," which allows us to act leniently in a case where two Halachic uncertainties exist. In this instance, it is possible that Halacha follows the view allowing the recitation of Birkat Kohanim at night, and even according to the other view, it is possible that the period of Ben Ha’shemashot is still Halachically considered daytime. The period of Ben Ha’shemashot is treated as a "Safek" – when we are uncertain whether it is daytime or nighttime – and thus there are two Halachic uncertainties relevant to the recitation of Birkat Kohanim during this period. As such, it is permissible to recite Birkat Kohanim until approximately 13-15 minutes after sundown, and the introductory blessing may be recited during that time, as well. This ruling is mentioned by Hacham David Yosef, in his Halacha Berura (vol. 6, p. 609; listen to audio recording for precise citation).
Summary: When Birkat Kohanim is recited at Minha or Ne’ila, it may be recited until 13-15 minutes after sundown, but not later than that time.
