King Hamad of Bahrain has asked his eldest son, Crown Prince Salman, to start a national dialogue to resolve the Gulf state's political crisis.
The prince, who earlier called on protesters to withdraw from the streets, is authorised to talk to all parties, a statement said.
Troops fired on demonstrators trying to march into the centre of the capital Manama on Friday, wounding at least 50.
US President Barack Obama has phoned King Hamad to urge restraint.
Bahrain, a close American ally, must respect the "universal rights" of its people and embrace "meaningful reform", he said.
Britain, the former colonial power, has joined the US in advising its citizens against all but essential travel to the kingdom.
Many of the protesters in Manama, which has a disaffected Shia Muslim majority, have been calling for the overthrow of the Sunni Muslim royal family.
But protest leaders are reported to have postponed an anti-government demonstration scheduled for Saturday.
Speaking on Bahrain state TV, Prince Salman expressed regret for "these painful days" and called for unity.
"We are at a crossroads," he said.
"Youths are going out on the street believing that they have no future in the country, while others are going out to express their love and loyalty. But this country is for you all, for the Shia and Sunnis."
As night fell in Manama, gunfire could still be heard. At one point on Friday, army units were seen firing anti-aircraft weapons over the heads of protesters in Manama.
The BBC's Caroline Hawley, in Manama, says the funeral procession of one of a protester killed earlier this week turned into another anti-government demonstration.
Mourners were trying to make their way to the Salmaniya Hospital, where their injured colleagues were being treated, when they came under fire close to Pearl Square.
The square in the centre of the capital has been sealed off by the army to prevent further large-scale demonstrations.
One protester, 27-year-old bank clerk Ali al-Haji, told the Associated Press news agency that live ammunition had been used.
"People started running in all directions and bullets were flying, I saw people getting shot in the legs, chest and one man was bleeding from his head," he said.
More than 120 people were admitted to hospital after the clashes, many suffering the effects of tear gas, some with broken bones and one person with a gunshot wound to the leg, medical officials told the BBC.
Bahrain's most senior Shia cleric, Sheikh Issa Qassem, has described attacks on protesters as a "massacre" and said the government had shut the door to dialogue.
Western countries have urged Bahrain to show restraint in dealing with protesters and called for meaningful reform in the small Gulf state kingdom.
While Bahrain is tiny, with a population of less than one million, it is home to the US Navy's Fifth Fleet and is near another key US ally in the region, Saudi Arabia.