* Algerians want new generation of leaders
* Oil and gas production unaffected by protests
* Biggest protest since unrest began last month
Hundreds of thousands of people crammed into central Algiers on Friday, Reuters witnesses said, in the biggest protests against President Abdelaziz Bouteflika's 20-year rule since unrest began last month.
Bouteflika on Monday reversed a decision to stand for another term after mass protests against him, but stopped short of relinquishing office and says he will stay on until a new constitution is adopted.
Algerians quickly rejected his offer and demanded that the 82-year-old president hand over power to a young generation of leaders who can create jobs and stamp out corruption
Protests have peaked on Fridays. They are also taking place in other cities.
"Those who think we are tired are wrong. Our protests will not stop," said doctor Madjid Benzida, 37, as police blocked streets leading to government offices and parliament.
Bouteflika has been losing allies in recent days since returning from medical treatment in Switzerland.
A senior FLN figure said in an interview on Thursday night the long-ruling president was "history now".
The remarks by Hocine Kheldoun to Ennahar television were another setback Bouteflika, who hoped to pacify Algerians by promising to take steps to change a political landscape that has been dominated by a ruling elite for decades.
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 had brought children: "I want a better future," said Mohamed Kemime, 10, draped in a national flag.
"Bouteflika and his men must go as soon as possible," said student Yazid Ammari, 23.
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.
Bouteflika has rarely been seen in public since suffering a stroke in 2013. Protesters say he is no longer in a fit state to rule.
The new prime minister, Noureddine Bedoui, said on Thursday he would form a temporary government of technocrats and others to work towards 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 suffered from the unrest. Its biggest oil field Hassi Messaoud and its Hassi Rmel gas field have not been affected, a source from state oil giant Sonatrach told Reuters.
Many Algerians say that the president and other veterans of the 1954-1962 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 money on the population, 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.
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