The foundation of the entire discussion is the command in Vayikra 2:13 — "you shall not omit from your grain offering the salt of your covenant with God" — which ties salt inseparably to the offering, calling it specifically "the salt of the covenant," and Bamidbar 18:19 extends this language to the priestly gifts, calling the arrangement "an everlasting covenant of salt before God," so that both the altar-rite and the hereditary priesthood share the same covenant-through-salt formula.
רש"ר הירש, ויקרא ב יג explains that salt symbolizes non-change (אי-השתנות), sealing what it touches against all external influences, and that this quality is precisely what makes it the natural symbol of a covenant — for, as רש"ר הירש, ויקרא ב יג elaborates, decay is the beginning of new formation, so salt's power to prevent decay represents existence without change; what is bound in covenant stands apart and is not subject to external forces that would alter it, and when the salt comes from communal funds it symbolizes the covenant held in the public trust, the entire people bearing responsibility for its eternal, unchanged perpetuation.
Rashi (Vayikra 2:13) traces the covenant all the way back to the six days of Creation, when the lower waters were promised a place at the altar through salt and through the water-libation on Sukkot, giving the "salt of the covenant" a primordial depth that precedes Sinai entirely, while Rashi (Bamidbar 18:19) characterizes the covenant with Aharon as made through something "healthy, enduring, and that strengthens others" — salt being the living metaphor for a bond that does not weaken over time.
The Ramban (Vayikra 2:13) draws out the covenantal architecture explicitly: the salt-covenant of the offerings becomes the paradigm (אב) for all other covenants, so that when Scripture calls the priestly gifts (Bamidbar 18:19) or the Davidic monarchy (Divrei HaYamim II 13:5) a "covenant of salt," the force of the expression is that they endure as the salt-covenant of the offerings endures — the eternal salt-covenant of the altar is the standard by which all permanent bonds are measured.
The Gemara (Menachot 20a) grounds salt's indispensability in that same covenantal language: Rabbi Yehuda holds that the word "covenant" (ברית) written in connection with salt ensures that offerings must always be salted, while Rabbi Shimon presses a verbal analogy between "an everlasting covenant of salt" (Bamidbar 18:19) and "a covenant of everlasting priesthood" (Bamidbar 25:13), concluding that just as no offering is possible without the priesthood, none is possible without salt — making the two eternal covenants structurally parallel and mutually illuminating.
The Kli Yakar (Vayikra 2:13) adds a dimension rooted in salt's natural paradox: it contains within itself both the quality of fire and the quality of water, i.e., both din and rachamim, and it is therefore called "your covenant with God" — for in the act of bringing the salted offering, Israel enters a covenant with God to place Him in sovereignty over all opposites, the unchanging salt presiding over a union of what would otherwise be at war.
Targum Jonathan (Bamidbar 18:19) renders the covenant "as the salt that seasons the flesh of the offerings — it endures forever before God," embedding the physical permanence of salt directly into the translation's definition of what an eternal covenant is, while the Ibn Ezra (Vayikra 2:13) reads the verse as God's declaration that He has brought Israel into a sworn covenant not to offer anything insipid, since doing so would constitute contempt.
Likkutei Torah, Vayikra probes the inner spiritual root of salt's covenantal role: salt itself has no taste yet imparts taste to meat, and its root (שרש) lies in the gevurot of Abba — born when heat transforms water — so that it operates as a force of refinement that draws sweetness from severity, an inner dynamic that undergirds why salt, and not some other preservative, is the vehicle for the altar's eternal covenant.
Rabbeinu Bahya (Bereishit 17:13) connects "brit melach olam" in a Kabbalistic reading to the divine attribute that is "the foundation of the world" (יסוד עולם), the sefirah that sustains all existence, so that salt's covenant becomes identified with the very principle of cosmic perpetuation — that which keeps the world from dissolution, just as salt keeps matter from decay.