Amadou Toumani Toure made the appeal on Saturday in a visit to Gao, 300km southeast of the town of Kidal where the rebels attacked and briefly occupied two army camps last month before withdrawing to surrounding mountains with stolen arms.
State television broadcast the president’s speech on Sunday.
The desert nomads, light-skinned, blue-turbaned warriors who staged revolts from Kidal in the 1960s and the early 1990s, want Mali's black African-dominated central government to grant them special status.
A peace deal was signed between the government and the rebels in 1998. Many former Tuareg rebels were subsequently integrated into the army but some have since deserted.
Mali's government says these deserters are behind the attack on Kidal.
While Tuaregs say they accept Toure's presidency and want to remain part of Mali, they demand that the government recognise their specific culture and identity.
Government forces resumed control of Kidal and are hunting the rebels, but Toure said in his appeal broadcast on state TV that there was still time to solve the dispute through talks.
"I tell my brothers who have taken up arms that it is not too late ... that it is still time to stop," he said.
"Family problems should be discussed first in the family. Let them [the rebels] first come back to the family to talk about their problems and we'll listen to them."
Some analysts fear that if the government attempts to subdue the rebels by force this could touch off another full-scale revolt by the Tuaregs, who have long complained of marginalisation by the government in Bamako.
Toure called on the rebels to think about what they were doing, "to weigh all the consequences that this could have on our unity and our cohesion and on the different communities which live in our country".
He made the appeal amid media reports that his government was asking neighbouring Algeria to mediate in the dispute.
Algeria and Libya have long competed for influence in Mali's north, a balance of power which has become all the more important since foreign oil companies started seriously prospecting in the region two years ago.
Consulate to close
Toure visited Libya last week for talks with the country's president, Muammar al-Qadhafi, who condemned the attack on Kidal by the Malian Tuaregs and said his government would close a consulate in the town which it opened this year.
The Tuaregs, a Berber people that was Islamised in the 16th century, have their own language and alphabet.
They can be found in Niger, Nigeria, Burkina Faso, Senegal and Mali. Orginally leading a nomadic existence, they have long been settled and no longer roam freely across the Sahara desert.