When Mali's democratically elected leader was ousted in a military coup in March, Tuareg rebels seized on the power vacuum and within weeks took control of the north, aided by an Islamist faction. The Islamists then quickly ousted the Tuaregs and took control of half the country.
The U.N. Security Council has unanimously approved the idea of an African-led military force to help the Malian army oust Islamic militants, but its details are still unclear.
One plan would see Mali's embattled government in the south and its West African neighbors taking the military lead to battle with the militants, with the United States and European countries in support.
Any military intervention would likely require Algeria, whose reforms have headed off the Arab Spring tumult experienced by neighbors such as Libya and Tunisia and left it with the strongest military and best intelligence in the region.
Clinton said she and Bouteflika spoke at length about Mali, with the Algerian leader appearing to caution against any rash action.
"I very much appreciated the president's analysis based on his long experience as to the many complicated factors that have to be addressed to deal with the internal insecurity in Mali and the terrorist and drug trafficking threat that is posed to the region and beyond," Clinton told reporters.
She said they agreed to continue discussions with the U.N. and African nations "to determine the most effective approaches that we should be taking."
Washington is keen to eliminate northern Mali as a haven for al-Qaida in the Islamic Maghreb, which may have been involved in September's attack on the U.S. Consulate in the Libyan city of Benghazi. Mali even came up in the U.S. election campaign, with Republican challenger Mitt Romney citing the African nation's instability in a foreign policy debate with President Barack Obama.
As further evidence of the U.S. intensifying its diplomatic work in Mali, Maria Otero, an undersecretary of state for civilian security, democracy and human rights, was to travel to Mali on Monday. She is the highest-ranking Obama administration official to visit since the coup. She'll meet with Mali's prime minister, human rights activists and internal refugees.
The 15-nation West African regional bloc, the Economic Community of West African States, or ECOWAS, has discussed sending 3,000 troops to help oust the Islamist militants from the north. Many, though, question how Mali's weak military could take the lead on such an intervention and analysts believe more ECOWAS soldiers would be needed to take and hold the France-sized desert area now controlled by the militants.
While the U.S. wants to see the rebels routed, it has no interest in active involvement in the military mission, unless Mali and West African states explicitly ask for such assistance, a senior American diplomat in Africa said. The official demanded anonymity because he wasn't authorized to speak publicly on the matter.
From Algeria, Clinton left for three days of talks in the Balkans, arriving Monday night in the Bosnian capital of Sarajevo.
She plans to join the European Union's top diplomat in meetings with the leaders of Bosnia, Serbia and Kosovo, urging those nations to make the necessary reforms to join the EU and NATO. She'll finish with meetings in Croatia and Albania, NATO's two newest members.