Tunisia's president has said he will not seek a new term in office in 2014, following widespread protests which have left at least 23 people dead.
Zine al-Abidine Ben Ali said he was also ordering police to stop using live rounds, hours after at least one person was shot dead in the capital Tunis.
Human rights groups say more than 60 people have died in weeks of unrest across the country.
Mr Ben Ali, 74, has ruled the country virtually unchallenged since 1987.
Speaking in his third nationally-televised address since the violence began, he said there was "no presidency for life" in Tunisia.
Many had expected him to amend the constitution to remove the upper age limit for presidential candidates and enable him to stand again in 2014, but he said he did not intend to do so.
The president, who earlier this week blamed the unrest on "terrorists", said he felt "very, very deep and massive regret" over the deaths of civilians in recent weeks.
He said he had ordered troops to stop firing on protesters except in self defence, saying: "I won't accept that another drop of blood of a Tunisian be spilled."
The speech also addressed other key concerns of the protesters, pledging "total freedom of the press and a removal of internet restrictions" and promising to take action on food prices, which have gone up fourfold in recent weeks.
The US, the EU and the UN have all criticised the government's response to the unrest and called on the security forces to show restraint.
The UK has advised against all non-essential travel to Tunisia while the protests continue.
The US has issued a similar warning, citing "intensifying political and social unrest in Tunisia".
Trade unions have called on people to observe a general strike on Friday in the capital and other areas.
Tunisia's main opposition leader, Najib Chebbi, welcomed the president's announcement, but said he was waiting to see "concrete details" of the plans.
Shortly after the speech was broadcast, crowds of Mr Ben Ali's supporters took to the streets of the capital, cheering and sounding car horns.
But other people said they did not yet believe the situation had been resolved.
"This morning, police were firing on people. At night everything changes. Something is not normal," one man told the Associated Press news agency.
The BBC's Adam Mynott in Tunis says the president still has a very sceptical nation to convince, despite his apparently contrite words, and that gunshots could be heard in the streets during the speech.
The fact that violent protests have erupted in towns all over the country shows how widespread the feeling of resentment towards the government is, says our correspondent, and it remains to be seen what response his comments will have.
The protests began in mid-December in the southern town of Sidi Bouzid, 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.
Over the past few weeks, protests have spread throughout the country, with troops opening fire on crowds on several occasions.
By Thursday, the protests had reached the heart of the city. At least one person was shot dead while AP said an American journalist was among the injured.
Officials say 23 people have been killed over the past few weeks but human rights groups put the figure at more than 60.
The government has previously blamed religious groups and opposition parties for stoking the violence.
Earlier this week, Mr Ben Ali dismissed his interior minister in an apparent attempt to stem the anger over the security forces response to protests.
He also said all those arrested during the protests would be released from prison and that he would establish a committee to investigate allegations of corruption.
Mr Ben Ali is only Tunisia's second president since the country gained independence from France in 1956.
He came to power in 1987 and was last re-elected to a five-year term in 2009 with 89.62% of the vote.