PARIS — For a third successive week, tens of thousands of people took to the streets of the capital and cities across Algeria on Friday to protest a fifth term for the country’s gravely ill president, Abdelaziz Bouteflika, as new cracks opened in the longstanding authoritarian regime.

Many of the protesters on Friday started marching even before the end of weekly prayers, a new development in what has become a wildfire popular revolt organized largely through social media.

The streets of Algiers were so packed with demonstrators that movement inside the crowds was impossible, observers reported. At one point crowds forced through barriers blocking access to the presidential palace, the Mouradia.

The demonstrations were largely nonviolent although there were some clashes between demonstrators and the police, who used tear gas. The police detained 195 people, Algerian state television reported.