France's President François Hollande called France's colonial rule of Algeria "unjust and brutal", speaking to the Algerian parliament on Thursday.
But he did not apologise for colonisation or repression during the independence war.
"Over 132 years Algeria was subjected to a profoundly unjust and brutal system," Hollande told Algerian MPs to applause. "This system has a name: it is colonialism and I recognise the suffering that colonialism inflicted on the Algerian people."
In the audience were numerous veterans from the 1954-1962 war of independence in which an estimated 1.5 million Algerians died.
On the second day of his visit to Algeria, Hollande said he had not come to say sorry for the crimes committed during the colonial period, as some Algerians, including a dozen political parties, have demanded.
Recognising what happened was a way to start a new era in bilateral relations, he said, insisting that nothing would come from "forgetfulness or denial".
The French president referred to specific atrocities, notably the massacre at Setif, where nationalist unrest at the end of World War II was brutally put down by French forces, leaving thousands dead.
And he spoke of "the violence, injustices, massacres and torture" during the independence war.
The French-language Algerian press hailed the visit for turning a page in relations, with the popular El-Watan daily saying Hollande had demonstrated "exceptional lucidity and sincerity, for a French president".
More than half a million Algerians live in France, and nearly 200,000 Algerians receive French visas every year, but many are frustrated at not being able to obtain them and seek a better life in Europe.
While saying that it was necessary to "manage the flow of migrants" Hollande promised to "better accommodate" Algerians seeking to move to France and to streamline the visa process, saying that doing so was of "mutual interest".
On Wednesday Hollande and Algerian President Abdelaziz Bouteflika signed a declaration of friendship and cooperation and five accords, including an agreement that French vehicle manufacturer Renault will build a factory near the western city of Oran.
In his address to parliament, Hollande stressed France was ready "to go further" in its cooperation with Algeria in the energy, healthy, environment, construction, and transport sectors.