Ouane called the attacks "acts of terrorism" carried out by drug-traffickers and arms smugglers and said all of these activities posed a threat to the security of whole region.
"The government of Mali knows that it can count on the political, diplomatic and material support of the countries and organisations that you represent," he told foreign ambassadors in a briefing on Saturday.
The anti-government group have ambushed three military convoys in the past week in the desolate mountain region of Tin-Zaouatene bordering Algeria and Niger.
Several dozen soldiers have been taken prisoner and vehicles and ammunition have been seized.
At least 13 people, most of them civilians, were also killed in recent days by landmines which the government says were laid by the group to cover their withdrawal after the attacks.
In Niger, the Tuareg-led Niger Movement for Justice (MNJ) group has killed more than 45 soldiers during a seven-month uprising in the uranium-rich north, prompting the government to declare a state of alert in Agadez, the country's largest city.
Mamadou Clazie Cissouma, the Malian defence minister, said there were links between the attacks in both countries.
"The information we have indicates that Ibrahim Bahanga's followers have taken part in the events in Niger and that, vice-versa, foreign individuals from Niger and elsewhere have participated in attacks and mine-laying [in Mali]," he said.
Niger's MNJ, which the government there describes as "bandits", has denied any alliance with the Malian Tuareg group.
Cissouma said the area around Tin-Zaouatene on the border was a major trans-Saharan drug-smuggling hub.
It was not immediately clear whether the international support Mali was seeking included military aid.
US military experts have trained armies in the Sahel - the border of the Sahara desert - and in Mali for several years as part of Washington's Trans-Sahara Counter-Terrorism Partnership (TSCTP), to bolster military co-operation and confront Muslim fighters.
Amadou Toumani, the Malian president, said Toure has called for a regional conference on security in the Sahel.
His counterpart in Niger, Mamadou Tandja, has asked Algeria, Libya and Sudan for support in ending the violence in the north.