Kheldoun, a former ruling party spokesman, became one of the most senior FLN officials to break with Bouteflika publicly, saying the party had to look forward and support the aims of demonstrators.
Some parents brought their children to Friday’s demonstration.
“I want a better future,” said Mohamed Kemime, 10, draped in a national flag.
One of Algeria’s most influential clerics appealed for patience.
“Let’s be optimistic, Algeria needs to overcome its crisis,” said Mohamed Abdelkader Haider from an Algiers mosque.
The new prime minister, Noureddine Bedoui, said on Thursday he would form a temporary government of technocrats and others to work toward political change, and he urged the opposition to join in a dialogue.
A former minister who is familiar with Bouteflika’s inner circle told Reuters that the president could not survive given the pressure building against him.
“Game over. Bouteflika has no choice but to quit now,” the former minister said on condition of anonymity.
Algeria is a major oil and gas producer, but so far exports have not been affected by the unrest. Its biggest oil field Hassi Messaoud and its Hassi Rmel gas field have been operating normally, a source from state oil giant Sonatrach told Reuters.
Many Algerians say that the president and other veterans of the 1954-62 war of independence against France have neglected them for decades.
The military, which has traditionally played a behind-the-scenes power broker role, has distanced itself from Bouteflika and stayed in its barracks throughout the crisis. It is expected to retain influence under all scenarios.
Algeria was relatively untouched when the 2011 “Arab Spring” uprisings swept away veteran autocrats in the Arab world. Bouteflika and his allies, effective manipulators of the opposition, managed to avoid major unrest by spending oil revenue on popular programs, such as handing out low interest loans and housing.
Bouteflika helped to defeat a civil war against Islamist insurgents in which tens of thousands of people were killed in the 1990s, and many Algerians long accepted heavy-handed rule as the price of stability.
But the public has lost patience with deteriorating economic conditions and the FLN’s failure to make the transition to a new generation despite the president’s failing health.