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In this paper, several characterizations of quasi-complemented posets in terms of Baer ideals, 0-ideals, and minimal prime ideals are obtained. This extends the results of Jayaram, Cornish and Varlet. Further, we investigate the connections between Baer ideals, 0-ideals, and minimal prime ideals in the class of [Formula: see text], which extends the results of Jayaram. Moreover, for a given meet-semilattice [Formula: see text] in the class [Formula: see text], we prove that [Formula: see text] is weakly quasi-complemented if and only if each minimal prime ideal in [Formula: see text] contracts to a minimal prime ideal in [Formula: see text]. This extends the result of Cornish to meet-semilattices.