But, with a combination of determination, realism and nimble political footwork, Mr Bouteflika has shown he is a power in his own right. The amnesty for some 5,000 Islamic militants that began this week is a first step to national reconciliation - a sign that Algeria may at last be about to move beyond the civil war unleashed by those same generals, when they cancelled the 1992 elections that the now outlawed Islamic Salvation Front (FIS) was about to win.
With long-overdue frankness, the President has revealed that not 26,000 (as claimed by the regime), or 70,000 (as estimated by foreign observers) but no fewer than 100,000 people died in the savage fighting that for most of the decade has made Algeria, a country of huge potential wealth and talent, an international outcast. That status, too, Mr Bouteflika wants to end. He has invited Jacques Chirac, leader of the former colonial power, to make an official visit, and has permitted Cheb Mami, Algeria's greatest popular music star, to give his first concert in his home country for 10 years.
But the amnesty, and the "law for civic concord" that will follow it, are the easy parts. The AIS, the largest Islamic guerrilla group and military wing of the FIS, may have made a truce with the government, but the FIS party itself remains banned. Until it is legalised, lasting political stability will remain an illusion. In the meantime the violence continues. Only this weekend, six army soldiers were shot dead in an ambush, allegedly the work of the most radical insurgent organisation, the GIA or Armed Islamic Group, which has rejected all calls for a ceasefire.
And then there is the army itself. Algeria's fundamental problem is that ultimate authority lies in the hands of the Le Pouvoir generals, self- appointed heirs of the liberation movement that won independence in 1962, but who have long since lost touch with the modern world. Every gesture of reconciliation by Mr Bouteflika towards the rebels risks upsetting the formidable faction within Le Pouvoir that insists on nothing less than total victory.
For this reason, the President plans to hold a referendum on the amnesty and on the new law. Not only will a popular endorsement make up for the near-farce of the April election. It will strengthen his hand with the military. As Mr Bouteflika knows, the average Algerian yearns for nothing so much as peace and normality. Having led the country into a bloody dead end by overturning the result of one election, the generals would be foolish indeed to ride roughshod over another expression of the public will.