Speaking following a meeting with Essid, Ghannouchi said that the new cabinet lineup "does not meet the aspirations of the Tunisians for a national unity government."
Ghannouchi voiced hope that ongoing consultations "will result in national consensus on the government lineup and program."
The Tunisian parliament was scheduled to hold a session on Tuesday to give confidence to Essid's new government, but the session was delayed.
The leftist Popular Front has already rejected Essid's government. The Afek Tounes party also said it would oppose the new government.
In Tunisia's 217-seat parliament, the secular Nidaa Tounes party holds 86 seats, while Ennahda holds 69. The Popular Front and Afek Tounes have 15 and eight seats respectively.