The custom of the Sepharadim is to conduct the Birkat Kohanim service during the Shaharit prayer as usual in the house of an Abel (mourner) during the seven days of mourning. However, if the Abel himself is a mourner, he should not recite Birkat Kohanim. He should instead leave the room at that point in the service, and not participate in the Beracha.
If no Kohanim are present in the house of the Abel, or if the community follows the custom not to recite Birkat Kohanim in a house of mourning, then the Hazan recites the passage, “Elokenu V’Elokeh Abotenu Barechenu Ba’beracha Ha’meshuleshet…” in place of Birkat Kohanim.
If a mourner who is a Kohen prays in the synagogue on Shabbat during the seven-day mourning period, then he should leave the synagogue at the time of Birkat Kohanim, rather than participate with the other Kohanim. However, if there are no other Kohanim present in the synagogue, then he should recite Birkat Kohanim. In such a case, refraining from reciting Birkat Kohanim would make a public spectacle of the Abel’s status of mourning. On Shabbat it is forbidden for a mourner to observe “Abelut Be’farhesya” – public expressions of mourning, and he should therefore recite Birkat Kohanim in the synagogue on Shabbat if no other Kohanim are present. If there are other Kohanim, however, then his non-participation is not readily noticeable, and he should therefore not take part in the Beracha.
A Kohen who is a mourner resumes his regular participation in Birkat Kohanim immediately after the seven-day mourning period. No distinction is made in this regard between mourning for parents and mourning for other relatives; in either instance, he resumes his participation in Birkat Kohanim upon the completion of the seven days.
Summary: The custom among Sepharadim is to recite Birkat Kohanim in a house of mourning, but if the mourner is a Kohen he should leave the room and not recite Birkat Kohanim. On Shabbat during the seven days of mourning, a mourner who is a Kohen does not recite Birkat Kohanim unless there are no other Kohanim in the synagogue. The mourner resumes his participation in Birkat Kohanim immediately after the seven days.