Question: How should one conduct himself if he is in the middle of davening when the sheliach tzibbur reaches Birkas Kohanim?
Discussion: This depends on exactly where in the middle of davening one is holding. One who is in the middle of reciting Birchos Kerias Shema or Kerias Shema itself should stop and listen to the blessings of Birkas Kohanim. He must also answer Amen to the actual blessings of the Kohanim, but not to the berachah of לְבָרֵךְ אֶת עַמּוֹ יִשְׂרָאֵל בְּאַהֲבָה.67
One who is davening Shemoneh Esrei when the sheliach tzibbur reaches Birkas Kohanim should stop and listen.68 However, he may not leave his place to face the Kohanim, nor may he answer Amen to the blessings of the Kohanim.69 Accordingly, one should not begin Shemoneh Esrei, unless he is sure he will finish before Birkas Kohanim.70 However, if one has already begun Shemoneh Esrei, he should not hasten his davening to finish before Birkas Kohanim.71
A Kohen should be sure to finish Shemoneh Esrei in time to perform Birkas Kohanim. He must also forgo responding to Kaddish, Kedushah, Barchu, and hearing Kerias HaTorah if doing so will interfere with his performance of Birkas Kohanim.72
67 Igros Moshe, Orach Chaim IV, 21:2; Teshuvos Vehanhagos I:78. [If one is holding bein haperakim, then one may even answer Amen to the berachah of לְבָרֵךְ אֶת עַמּוֹ יִשְׂרָאֵל בְּאַהֲבָה; see Mishnah Berurah 66:23, and Ishei Yisrael 19:11.]
68 Igros Moshe ibid.; R’ S. Z. Auerbach cited in Halichos Shlomo, Tefillah 10:3. Reportedly this was also the custom of the Chazon Ish; see Shevet Hakehasi I:79. However, a minority opinion maintains that one need not stop in the middle of Shemoneh Esrei and will still be included in the blessings of the Kohanim; see Ashrei Ha’ish, Orach Chaim I, 23:7.
69 Igros Moshe ibid. (Cf. Igros Moshe, Orach Chaim V, 20:23, where he rules that one may even leave his place during Shemoneh Esrei to face the Kohanim.) However, if one is standing behind the Kohanim, it is proper for him to turn his face toward them; Halichos Shlomo Tefillah 10, Devar Halachah 7.
70 Igros Moshe Orach Chaim IV, 21:2; However, see Ashrei Ha’ish, Orach Chaim I, 23:6.
71 R’ Y. S. Elyashiv cited in Ashrei Ha’ish, Orach Chaim I, 23:6
72 R’ Y. S. Elyashiv cited in Ashrei Ha’ish, Orach Chaim I, 23:6 and 8.