In the 13-minute message posted to jihadist websites, Al-Qaeda in the Islamic Maghreb leader Abu Musab Abdul Wadud purportedly urges Tunisians to overthrow President Zine al-Abidine Ben Ali, who has ruled Tunisia since 1987.
"Send your children to us for training on how to use weapons and to get military experience," said the message.
It called on all Tunisians "to bring down Ben Ali's corrupt, criminal and tyrannical regime" and introduce Islamic law in the North African country.
US SITE intelligence said the message also praised anti-government protesters in neighbouring Algeria, where youths took to streets to protest rising prices of staples like sugar and cooking oil.
Tunisia has come under increasing pressure from the United States and other nations to curb its violent response to the month-long protests.
On Friday, the official news agency said Ben Ali had dismissed the government and dissolved parliament, promising to hold elections in six months.
Tunisian state television reported that a state of emergency had been declared "to protect the Tunisian people" and a ban on gatherings imposed.
The move came after thousands protested in the capital Tunis, urging Ben Ali to quit.
Police fired tear gas at the crowds outside the interior ministry.
Ben Ali late on Thursday announced he would stand down in 2014 and not run again for the presidency, but the protesters say he should go immediately.
Doctors say that 13 people were killed in overnight clashes in the capital and five protesters died on Friday even though Ben Ali said he had told security forces not to fire live ammunition at the protesters.
Ben Ali on Wednesday had sacked interior minister Belhaj Kacem, who was responsible for the much-criticised police force.