The Constitutional Council was expected to convene Wednesday to formalize his departure.
After Mr Gaid Salah's call for the implementation of Article 102 we had expected the process to begin very soon, but the week since has shown the Bouteflika clan's determination to play for time.
Hundreds of thousands of Algerians have taken to the streets since 22 February to protest against Bouteflika running for a fifth term in office, calling for the removal of the president and the government.
Faced with massive street protests across the North African country, a succession of veteran Bouteflika loyalists have deserted the president in recent days. Gaid Salah kept his position in a new government named Sunday, though it is unclear why.
His resignation caps six weeks of peaceful marches by protesters who wanted not just Bouteflika but the entire system to make an exit.
However, more than two-thirds of Algerians are now under 30, and are seeking a more "democratic Algeria" as they chanted in the protests.
The Defense Ministry statement Tuesday appeared to be a final warning, and the catalyst for Bouteflika's resignation.
The future of Algeria is up to its people, the United States said on Tuesday, after veteran president Abdelaziz Bouteflika resigned under pressure from the military. Bouteflika has ruled the country since 1999, despite promising in 2012 to step down after his third term.
The insurgency then linked up with al-Qaida and metastasized into a Sahara-wide extremist movement.
"I have taken this step because I am keen to put an end to the current bickering", Bouteflika said in a letter released on state media, using his main means of communication since suffering a stroke in 2013 and largely disappearing from public view.
On Monday, Bouteflika vowed to step down as president before his fourth term officially expires later this month. The opposition, which has lost its credibility by remaining too passive, even by participating in power, could it find a real leader?
Algerian demonstrators stage a protest in Algiers, Algeria, April 2, 2019.
Since 2014 Haddad was the president of the Business Leaders Forum, Algeria's leading employers' organisation but he quit the post on Thursday as criticism mounted against him for supporting Bouteflika.
The announcement on Bouteflika's resignation "doesn't change anything", psychology student Meriem Medjdoub said as she marched in central Algiers with around 1,000 protesters. Placard, center, reads, "when the system fails we have to make justice by ourselves".