Mali's sovereignty over almost all of its territory will be restored within "a few days", French President Francois Hollande promised as French troops prepare to pull out.
The announcement came as Paris scrambled Wednesday to verify a claim by Al-Qaeda's north African branch that it had executed a French hostage in retaliation for France's military intervention in Mali.
"In the last phase where we are, almost the entire territory will return to Mali's sovereignty in a few days," Hollande said during a dinner with representatives of the Jewish community in France.
Hollande spoke shortly after his Prime Minister Jean-Marc Ayrault told parliament that French troops would begin pulling out of troubled Mali "from the end of April".
Ayrault said a meeting next Monday between lawmakers in France's National Assembly and Senate would assess the involvement of French troops to help flush out Islamist rebels in the west African country "even if our troops will begin coming home from the end of April".
US Defense Secretary Chuck Hagel hailed France's military intervention in Mali in a phone call with his French counterpart, Jean-Yves Le Drian, thanking Paris for its "active leadership", officials said.
France sent troops to Mali on January 11 to prevent Islamists in the north from pushing south to the capital Bamako.
After initially hesitating, the United States has backed the French-led action with logistical support, sending transport planes, surveillance drones and refueling tankers to boost the campaign.
However France's actions have made its nationals targets for Islamist militants in the region.
A man claiming to be a spokesman for Al-Qaeda in the Islamic Maghreb (AQIM) told Mauritania's ANI news agency late Tuesday that "spy" Philippe Verdon had been executed in Mali on March 10 "in response to France's intervention in northern Mali".
"The French President Hollande is responsible for the lives of the other French hostages," the spokesman warned.
The French foreign ministry said it was trying to verify the report. "We can't say at the moment if it is credible," said a spokesman.
Verdon's father Jean-Pierre Verdon said he feared the worst. "I'm not under any illusion, but I will wait for confirmation," he told AFP.
In all 15 French nationals, including Verdon, are being held captive in Africa, with AQIM claiming responsibility for six of the kidnappings.
Verdon was seized on the night of November 24, 2011 along with Serge Lazarevic from their hotel in Hombori, northeastern Mali, while they were on a business trip.
The families denied that the two men were mercenaries or spies.
Extremist groups often use the private news agency ANI to distribute their statements or claims, which often turn out to be accurate.
The French hostages' families have in recent weeks expressed growing fears for their loved ones in the light of France's military offensive aimed at routing Islamists from northern Mali.
"We will do everything to free our hostages," French PM Ayrault told parliament on Wednesday.
France has in the past authorised the payment of ransoms to kidnappers in order to secure the release of its nationals, but officials say that has stopped since Hollande came to power last year.
France now has more than 4,000 troops on the ground in Mali, of whom about 1,200 are currently deployed in the northeast, carrying out clean-up operations after driving out most of the Islamist rebels from the area.
Hollande had already said he planned to scale back French military presence in the former colony from next month and start handing over responsibility to Malian troops and an African stabilisation force.
Five French soldiers have died in combat since the start of the operations.
There are still pockets of resistance in some areas such as the main northern city of Gao, which have witnessed stray attacks and suicide bombings since the Islamists fled.
The French troops in the region are backed up by African forces. Soldiers from Chad, whose experience and training has made them key in the French-led offensive, have also suffered casualties with at least 26 deaths.
On Tuesday the French army announced that 15 Islamist fighters had been killed in recent days in the northern Mali region of Gao, with the seizure of a large cache of arms and ammunition.
The AQIM source cited by the Mauritanian news agency refused to confirm reports that top Islamist rebels Mokhtar Belmokhtar and Abdelhamid Abou Zeid had been killed in Mali earlier this month.
France has been carrying out DNA tests to determine whether the militant leaders are among those killed in recent fighting in Mali.
Also on Wednesday, France's foreign ministry spokesman called for the "immediate release" of Malian journalist Boukary Daou, who was arrested this week for "incitement to disobedience" after publishing a letter criticising the new government salary earned by a former junta chief.
Mali's media have said they are boycotting government coverage in protest at the detention.