Siman 287

We say in Shabbat (12a): That Beit Shammai prohibit comforting mourners and visiting the sick on Shabbat, because he is pained (Rashi), and also so that he will not come to cry out on Shabbat (the Rif). And Beit Hillel permit it, because this is included in the category of gemilut chasadim, and furthermore, it eases the pain from them. And only with difficulty did they permit comforting mourners and visiting the sick on Shabbat for the reasons that have been explained, but the sages permitted it as has been written. However, those who do not go during the weekdays, but only on Shabbat—they do not act properly (Magen Avraham), unless it is someone who is preoccupied during the weekdays such that it is impossible for him to go (Sha'arei Teshuva).

The Rabbis taught: One who enters to visit the sick says, "It is Shabbat, from crying out [one must refrain], and healing is soon to come by the merit of Shabbat," and he should broaden their minds with comforts (Rashi). And this refers to a sick person who is not in immediate danger today, for if he is in immediate danger today, it is permitted to cry out and supplicate on Shabbat, as written in siman 576. And Rabbi Meir says the visitor should say: "Shabbat is able (the Rif) to have mercy," if you honor it by not grieving on it (Rashi). Rabbi Yehuda says he should say: "May the Omnipresent have mercy upon you and upon the sick of Israel," for the merit of the many is great. Rabbi Yose says he should say: "May the Omnipresent have mercy upon you among the sick of Israel," for when he includes him with the others, it is much better. Shevna of Jerusalem, upon his entry to the sick person, says "Shalom," and upon his departure says: "It is Shabbat, from crying out [one must refrain], and healing is soon to come, and His mercies are many, and may His Shabbat be in peace." And the Rambam in chapter 24 wrote according to the wording of the first Tanna, and the Tur and the Shulchan Aruch wrote according to the wording of Shevna, for he did not come to disagree but only to add a little, and our custom is like the Rambam. And likewise when they make a "Mi Shebeirach" for the sick in the synagogue, one should not say as on a weekday: "May the Omnipresent send healing," but rather "It is Shabbat, from crying out etc." (the Gra"z). But among us they bless "and may He send him a complete healing... it is Shabbat, from crying out etc.," and so it is printed in the prayer books. And I do not know who permitted this to them, if not for a very dangerously sick person, who is in immediate danger today as I have written.

The Shas did not mention which wording to say for the comforting of mourners, and it appears that one may say as on a weekday: "May the Omnipresent comfort you among etc." However, some say that one should say as with a sick person: "It is Shabbat from comforting, and comfort is soon to come, and His mercies are many, and may His Shabbat be in peace" (Rashal and Bach), and see Yoreh Deah siman 393, and among us it is not the custom to perform the comforting of mourners on Shabbat.