"Malian public opinion needs him," a diplomatic source told RFI as Keita quit the Elysée Palace without a word to the media.
A French presidential statement stressed that Keita "has made reconciliation his top priority" after the French-led defeat of the rebellion of Islamists and Tuareg separatists that at one point took control of the north of the country.
"We must remain vigilant" over the "terrorist threat", the statement said.
Although calm had returned on Tuesday morning, violence broke out in between Tuareg nationalists and Malian troops in Kidal at the weekend and there was a suicide attack in Timbuktu on Saturday.
Al Qaeda in the Isamic Maghreb has claimed responsibility for the Timbuktu attack.
Shots were fired on Monday at the Kati military base near Bamako by a group of soldiers who had been involved in last year's military coup and claimed to have been overlooked in the latest promotions to be announced.
Defence Minister Soumeylou Boubèye Maiga met them on Monday evening and promised to examine their cases, RFI's correspondent reports.
The French presidency judged it "natural" that there should be "tension" and "sporadic pockets of terrorism" in a country that is "convalescent and in the process of reconstruction".