Operation Gustav, one of France's largest actions since its intervention in its former colony, involves dozens of tanks, helicopters and aircraft, said General Bernard Barrera, commander of the French land forces in Mali, on Monday.
"We surrounded the valley north of Gao, which we believe serves as a logistics base for jihadist groups, and we began to search methodically," said Barrera, who is based in Gao, the largest settlement in northeastern Mali.
The city, 1,200 kilometres (750 miles) from the capital Bamako, was a stronghold of the Movement for Oneness and Jihad in West Africa (MUJAO), one of the Islamist militias which occupied the north until French-led forces dislodged them in January.
It suffered the first suicide bombings in Mali's history in February and has been the scene of deadly clashes between French-Malian forces and jihadists over the last two weeks.
No Islamist fighters were encountered on the first day of Operation Gustav, launched at dawn on Sunday, but troops said they neutralised around 340 artillery shells and high-calibre rockets and destroyed a Toyota pick-up truck.
All access points to the valley were shut off and its ridges secured at 6:00 am (local and GMT) on Sunday.
France's 3rd Mechanised Brigade later began the excavation of a thick forest where military intelligence suspects a jihadist base may be hidden.
French soldiers will spend the coming days combing the 20-kilometre (12-mile) valley with the help of Malian soldiers and police officers going into the nomad camps and mud houses which line the dry river basin.
"This is the fourth wadi we have gone into in the Gao region. There will no doubt be other such operations but perhaps not to the same extent," Barrera said.
Ethnic Tuareg rebels seized the country's vast arid north in the chaos following a coup in Bamako in March 2012 before losing control to well-armed Islamists.
A French-led intervention quickly drove insurgents from most of their northern strongholds, but significant pockets of resistance remain in Gao, as well as in the fabled desert city of Timbuktu.
"We have defeated the jihadist groups further north in the Ifoghas (mountains). There are none there anymore," Barrera told reporters.
"We are now operating in north-central Mali, to break the enemy by denying it time to reorganise."
'This isn't over'
Listening to audio recordings, flying observation missions and cross-checking with information from witnesses, French intelligence officials have concluded that the forested "wadi", or dry river basin, would be perfect for concealing weapons stockpiles.
The fighters themselves, whom France believes were present just days ago, may have moved to another valley, under cover of a sandstorm that raged the previous two days.
Colonel Bruno Bert, who is commanding the mission, warned against complacency.
"Many times these guys have hidden themselves for hours just a few metres away from us, and then suddenly stood up and opened fire," he said.
"This isn't over. This valley is big, with many secondary wadis. We will take however long we need to complete the search."
On Sunday night tanks stationed on ridges trained their night vision instruments on the valley floor while aircraft with thermal cameras patrolled the skies to ensure that militants could not escape under the cloak of darkness.
France is to start withdrawing its 4,000 troops from Mali at the end of April, and plans to leave a "support force" of 1,000 soldiers after elections promised for July.
Ministers from member states of the west African franc zone heard at a seminar in the Senegalese capital Dakar on Monday that the Malian economy shrank by 1.2% in 2012 because of the crisis.
French finance minister Pierre Moscovici confirmed that a donor conference co-chaired by the European Commission and France would be held in Brussels on May 15 to raise cash to "repair the damage caused by the war".
The war in Mali has also heightened fears that the conflict could spill over into other countries around the Sahel.
UN secretary general Ban Ki-moon on Monday issued an urgent call to reach an agreement between the independence movement and Morocco over Western Sahara.
"The rise of instability and insecurity in and around the Sahel requires an urgent settlement of this long-standing dispute," Ban said in a report to the UN Security Council.
"All governments consulted raised serious concerns over the risk that the fighting in Mali could spill over into neighbouring countries and contribute to radicalizing the Western Saharan refugee camps," Ban said.