PARIS — Tens of thousands of protesters in Algeria turned out Friday to demonstrate against the government’s latest attempt to pull the country out of its political impasse, clearly signaling popular rejection of a compromise offer by the Army this week.

The demonstration, the sixth in a row, appeared to reinforce the deadlock: protesters have dismissed the proposal from the country’s most powerful figure, Gen. Ahmed Gaïd Salah, the army chief of staff, to sideline the ailing president, Abdelaziz Bouteflika, install as interim president the head of the Senate, and hold elections.

What happens next is unclear, but some opposition figures said it was now up to the government to make what one called a more serious offer. The crowds in the streets, increasingly pressing in their demands, want the wholesale removal of what they call “the System” — everyone associated with Mr. Bouteflika’s 20-year reign. So far the government has given no sign of conceding.

In proposing Mr. Bouteflika’s removal, General Gaïd Salah, who had been the president’s staunchest ally, went beyond what many had expected. But by invoking Article 102, of the Algerian constitution, a section that calls for the removal of the president if he is found unfit, the general left the rest of the ruling “System” in place — unacceptable in the eyes of many Algerians.