אורח חיים ר׳Orach Chayim 200

Se’if 1א׳

שְׁלֹשָׁה שֶׁאָכְלוּ כְּאֶחָד, אֶחָד מַפְסִיק עַל כָּרְחוֹ לִשְׁנַיִם וְעוֹנֶה עִמָּהֶם בִּרְכַּת זִמּוּן. וַאֲפִלּוּ לֹא רָצָה לְהַפְסִיק, מְזַמְּנִין עָלָיו בֵּין עוֹנֶה בֵּין אֵינוֹ עוֹנֶה כָּל שֶׁהוּא עוֹמֵד שָׁם. אֲבָל שְׁנַיִם אֵין חַיָּבִים לְהַפְסִיק לְאֶחָד, הִלְכָּךְ אֵין חִיּוּב זִמּוּן חָל עַד שֶׁיִּתְרַצּוּ לְהַפְסִיק לְאֶחָד וּלְבָרֵךְ, וְאִם לֹא רָצוּ לְהַפְסִיק וְזִמֵּן הוּא עֲלֵיהֶם, לֹא עָשָׂה כְּלוּם; וְאִם לֹא רָצוּ לְהַפְסִיק, אַף הוּא אֵינוֹ רַשַּׁאי לְבָרֵךְ וְלָצֵאת לַשּׁוּק, עַד שֶׁיִּגְמְרוּ הַשְּׁנַיִם וִיזַמֵּן עֲלֵיהֶם, שֶׁהֲרֵי כְּבַר נִתְחַיֵּב הוּא בְּזִמּוּן וְהֵיאָךְ יְבָרֵךְ בְּלֹא זִמּוּן.

Laws of One Who Interrupts in Order to Bless — 2 paragraphs. Three people who ate together: one is obligated, even against his will, to interrupt for the two others and recite with them the zimun blessing. Even if he does not want to interrupt, they may perform zimun with him whether he responds or not, as long as he is still present. But two people are not obligated to interrupt for one, therefore the obligation of zimun does not take effect until they agree to interrupt for the one and to bless. If they do not wish to interrupt and he performs zimun with them, he accomplishes nothing. And if they do not wish to interrupt, he is also not permitted to bless and go out to the market until the two have finished and he performs zimun with them — for he has already become obligated in zimun, so how can he bless without zimun?

Se’if 2ב׳

אֵינוֹ צָרִיךְ לְהַפְסִיק אֶלָּא עַד שֶׁיֹּאמַר: בָּרוּךְ שֶׁאָכַלְנוּ מִשֶּׁלּוֹ וְכו', הַגָּה: וְיֵשׁ אוֹמְרִים שֶׁצָּרִיךְ לְהַפְסִיק עַד שֶׁיֹּאמַר: הַזָּן אֶת הַכֹּל, וְכֵן נוֹהֲגִין (הָרֹא"שׁ וְתוס' והר"י בְּשֵׁם בה"ג וְהַטּוּר). וְאִם הָיָה דַּעְתּוֹ לַחֲזֹר וְלֶאֱכֹל פַּת, אַף עַל פִּי שֶׁלֹּא אָכַל אַחַר כָּךְ, כְּשֶׁרוֹצֶה לְבָרֵךְ מְבָרֵךְ מִתְּחִלָּה בִּרְכַּת הַזָּן; וְכָל שֶׁכֵּן אִם חָזַר וְאָכַל (הר"י פֶּרֶק ג' שֶׁאָכְלוּ) (טוּר) וְחוֹזֵר וְגוֹמֵר סְעוּדָתוֹ בְּלֹא בְּרָכָה בִּתְחִלָּה.

He only needs to interrupt until they say: "Blessed is He from Whose bounty we have eaten," (baroukh cheakhalnou mitouvo) etc. Rema: And some say that he must remain until they say: "Who nourishes all," (hazon et hakol) and this is the common custom (Rosh, Tosafot, R’ Yitzḥak in the name of the Baal HaHalakhot Gedolot, and the Tur). And if his intention was to return and eat bread, even if in the end he did not eat again — when he wishes to recite Birkat Hamazon, he begins from the blessing HaZan ("Who nourishes"), and all the more so if he actually did return and eat (R’ Yitzḥak, chapter "Three Who Ate") (Tur), and he may resume and finish his meal without repeating the opening blessing.