President Emmanuel Macron regrets the misunderstandings from comments he made about Algeria, a French official said on Tuesday.
It was an indication that Paris may be trying to calm relations with its former colony.
Ties between Paris and Algiers have been badly strained in recent weeks after Mr Macron questioned whether there had been an Algerian nation before French colonial rule, and that Algeria's "politico-military system" had rewritten the history of its colonisation based on "a hatred of France".
That prompted Algiers to close its airspace to France's military, which is fighting in neighbouring Mali, and recall its ambassador.
Algerian President Abdelmadjid Tebboune said on Saturday that he would not make the first step to ease tension, telling German magazine Der Spiegel that Mr Macron had "opened an old conflict in a completely ridiculous way".
The relationship between the two countries is scarred by the trauma of the 1954-1962 war of independence in which the North African country broke from France.
Hundreds of thousands of Algerians were killed and both sides used torture.
Before a conference on Libya on Friday, to which Mr Tebboune had been invited, a French presidential official said Algiers was a key actor in the region and Mr Macron wanted him to attend.
The official sought to express Mr Macron's regrets after the comments he made to a group of young people who were working on the historical differences between the two countries.
"The president regrets the controversies and misunderstandings generated by the remarks reported and I will add that President Macron has the greatest respect for the Algerian nation, its history and the sovereignty of Algeria," the official said.
"He is strongly attached to the development of our two countries bilaterally for the benefit of the Algerian and French populations, and also to meet the great regional challenge, starting with Libya."
Mr Macron has pushed for more transparency about France's past with Algeria and has commissioned a report from historian Benjamin Stora.
It called for a truth commission over the war, but the French leader has ruled out issuing any official apology.