Thousands rallied in Tunis and other cities yesterday, while hundreds of protesters backed by the UGTT union launched a march on the capital from the impoverished region where an uprising began last month, ending strongman Zine El Abidine Ben Ali's 23-year rule.
Participants at the march called their protest a "caravan of liberation".
"The aim of this caravan is to make the government fall," said Rabia Slimane, 40, a teacher from Menzel Bouzaiane, where the first victim of the uprising was killed by security forces last month.
The peaceful anti-government demonstrators in Tunis were joined by hundreds of police officers, some of whom briefly blocked a car carrying interim president Foued Mebazaa, the speaker of parliament.
Public assemblies of more than three people are officially banned under a state of emergency that remains in place, along with a night-time curfew.
The General Union of Tunisian Workers (UGTT under its French acronym), which played a vital role in the movement against Ben Ali, has refused to recognise the new government because of its inclusion of figures from the old regime.
Ghannouchi has been prime minister in Tunisia since 1999.