Thousands of demonstrators are on the streets of the Tunisian capital, calling for the president to stand down immediately.
On Thursday night, Mr Ben Ali - who has governed
His speech came after weeks of protests that have left at least 23 dead.
A BBC correspondent in
Between 6,000 and 7,000 people joined a demonstration outside the interior ministry.
The numbers are unprecedented, says the BBC's Adam Mynott, who is at the scene.
Mr Ben Ali pledged to take action on food prices and end internet censorshipHuman rights groups say more than 60 people have died in weeks of unrest across the country, as security forces cracked down on protests over corruption, unemployment and high food prices.
The demonstrators have called on Mr Ben Ali to go, saying
This is in reaction to the president's pledge to quit in 2014, our correspondent says, but probably not the reaction he was expecting.
Trade unions called on people to observe a general strike on Friday.
There is now a public clamour for change, Adam Mynott says, which has become a tide which will be very difficult to hold back.
A BBC Arabic reporter in
Tourists going homeMeanwhile,
Thomas Cook and another holiday company, Thomson First Choice, are cancelling departures to
Tourism is key to
"The situation is unpredictable and there is the potential for violence to flare up, raising the risk of getting caught up in demonstrations," the UK Foreign Office said in its latest travel advisory.
In his speech on Thursday night, Mr Ben Ali said there was "no presidency for life" in
However, our correspondent says there is a degree of scepticism as to whether deeds will follow on from words.
Tunisian commentator Intissar Kherigi told the BBC Mr Ben Ali's time in office had been marked by continued infringements of human rights.
"During this time, there's been sustained human rights violations; torture, disappearance of journalists, of political opposition, all banning of all independent organisations, trade unions," he asserted.
"Not a single human rights organisation is allowed to operate freely in the country... So unfortunately the record does not really give us much hope."
'Terrorists'Mr Ben Ali, 74, is only
In Thursday night's speech he said he did not intend to amend the constitution to remove the upper age limit for presidential candidates, which would have allowed him to stand for a further term in 2014.
The president, who earlier this week had blamed the unrest on "terrorists", also said he felt "very, very deep and massive regret" over the deaths of civilians in the protests.
He said he had ordered troops to stop firing on protesters except in self defence, and pledged to take action on food prices, which have gone up fourfold in recent weeks.
Afterwards, Mr Ben Ali's supporters took to the streets of
In a further overture, foreign minister Kamel Mourjane said it would be possible to form a government of national unity involving the opposition.
Mustapha Ben Jaafar, head of the Democratic Forum for Work and Liberties, said the speech "opens up possibilities".
But human rights activist Mohamed Abbou said he believed President Ben Ali was "fooling the Tunisians with promises that have no tomorrow".
'Educate workforce'On Thursday,
Mrs Clinton was speaking in
"It is hard to have the kind of economic climate that is needed without making some of the social reforms that are required," she said.
"Put aside the critical issue of political freedoms, human rights and democracy that we have been discussing, focus on social conditions.
If you do not have an educated workforce, it is very hard to grow the economy to the extent that it should grow."
The protests in
Earlier this week, Mr Ben Ali sacked his interior minister and promised to create 300,000 new jobs.