The overnight strikes in Kidal came 24 hours after French-led troops seized Gao, the most populated town in Mali's Islamist-controlled arid north, which is roughly the size of Texas. Gao is home to about 60,000 people.
"There were air raids on Islamist bases in Kidal," 1,500 kilometres (940 miles) north of the capital Bamako, a Malian security source said, adding that the home of Ansar Dine (Defenders of the Faith) chief Iyad Ag Ghaly was destroyed.
A local official and residents gave similar accounts.
Kidal has been a bastion of Ansar Dine, whose leader Iyad Ag Ghaly is a former soldier and a Tuareg ex-rebel, who formed the group last year.
In April last year after a coup in Bamako, an alliance of Tuareg rebels seeking an independent homeland in the north joined forces with several Islamist groups, seizing Kidal first and then the northern towns of Gao and Timbuktu.
The Islamists quickly sidelined the Tuaregs, imposing a harsh version of Islamic sharia law in the region. Transgressors were flogged, stoned and executed, they banned music and television and forced women to wear veils.
France launched a military offensive on January 11 after Islamists captured a central town and pushed deeper into government territory towards the capital
French Prime Minister Jean-Marc Ayrault said the troops, having captured Gao, were advancing on Timbuktu, another key town held by Al Qaeda-linked rebels and a centre of Islamic learning for centuries.
Washington meanwhile decided to step up its role in the conflict by helping refuel French warplanes.
Washington's decision to agree to France's request for air refuelling facilities came after two weeks of deliberation. US Defense Secretary Leon Panetta gave the news to his French counterpart, Jean-Yves Le Drian in a telephone conversation Saturday, a Pentagon spokesman said.
They also discussed plans for the Americans to transport troops from African nations, including Chad and Togo, to facilitate the international effort in Mali.
The US military has an unparalleled fleet of more than 400 tankers equipped to refuel fighters and other warplanes in mid-air. France has about 14 such tankers.