Morocco, formerly a French colony, is a close ally of France and the two countries have strong commercial and cultural ties.
Rabat reacted furiously to the two lawsuits filed by an NGO against against Abdellatif Hammouchi, the head of Morocco’s domestic intelligence agency (DGST).
Hollande phoned the king, who is currently touring West Africa, to reassure him of France's "constant friendship," and "dispel the misunderstandings," the French presidency said on Tuesday.
He also underlined his desire to "strengthen the partnership between the two countries."
After the lawsuits were filed, seven French policemen arrived at the Moroccan ambassador's residence to inform Hammouchi who was at the time accompanying the interior minister on a visit to Paris, of a summons issued by the investigating judge.
On the same day, Spanish actor Javier Bardem, was quoted by French media citing diplomatically embarrassing comments about Morocco allegedly made three years ago by the French ambassador to the United Nations.
"Morocco is a mistress who you sleep with every night, who you don't particularly love but you have to defend," Bardem quoted him as saying, at the launch in Paris of his new documentary on Western Sahara, "Sons Of The Clouds, The Last Colony."
Morocco summoned the French ambassador on Friday to reject the torture allegations and vigorously protest the lawsuits while describing the alleged comments by France's UN envoy as "scandalous and unacceptable."
The French foreign ministry moved swiftly to contain the fallout, saying on Saturday that the police visit to the ambassador's residence was a "regrettable incident" and promising to shed light on the matter. It also categorically rejected Bardem's comments.
On Monday the French foreign ministry received Moroccan ambassador Chakib Benmoussa.
The two cases that sparked the diplomatic spat were filed by Action by Christians for the Abolition of Torture (ACAT), an NGO based in Paris.
They relate to a pro-independence Sahrawi activist, Ennaama Asfari, who was handed a 30-year jail term in 2013 by a Moroccan military tribunal on the basis of confessions allegedly signed under torture.
On Monday ACAT sharply criticised the French foreign ministry, insisting that "in a democracy" diplomacy has "absolutely no right to interfere in the work of the judiciary."
A UN special investigator said in 2012 that the torture or cruel and inhumane treatment of detainees in Morocco was "very frequent".