Prime Minister Mohammed Ghannouchi said he would be taking over from President Zine al-Abidine Ben Ali.
A state of emergency has been declared amid protests over corruption, unemployment and rising prices.
Reports say Mr Ben Ali has left the country, but this has yet to be confirmed by officials.
Earlier, police fired tear gas as thousands of protesters gathered outside the interior ministry.
Doctors say that 13 people were killed in overnight clashes in Tunis, and there are unconfirmed reports that five people have been killed in protests on Friday outside the capital.
In an address on state television, Mr Ghannouchi said: “Since the president is temporarily unable to exercise his duties, it has been decided that the prime minister will exercise temporarily the duties.”
Mr Ghannouchi, 69, a former finance minister who has been prime minister since 1999, will serve as interim president.
Earlier, the president – who had said in a TV address on Thursday night that he would relinquish power in 2014 – said he was dismissing the government and dissolving parliament, and that new elections would be held within six months.
The state of emergency decree bans more than three people from gathering together in the open, and imposes a night-time curfew. Security forces have been authorised to open fire on people not obeying their orders.
Human rights groups say dozens of people have died in recent weeks as unrest has swept the country and security forces have cracked down on the protests.
The protests started after an unemployed graduate set himself on fire when police tried to prevent him from selling vegetables without a permit. He died a few weeks later.