Secretary of State Hillary Rodham Clinton and President Abdelaziz Bouteflika of Algeria, right, discussed ways to counter a regional crisis.

After the meetings, American officials asserted that the Algerians’ and Americans’ political and military approaches to the crisis had begun to converge, but that more work was needed. “We have agreed to continue with in-depth expert discussions,” Mrs. Clinton said, “to determine the most effective approaches that we should be taking.”

The Islamist takeover of northern Mali is a growing worry for the United States and for France, the former colonial power, which maintains an interest in West Africa and has been pressing for international action.

Earlier this month, the United Nations Security Council adopted a resolution underscoring its “readiness” to send an international force to evict the militants in response to a request from a Mali government. While a military plan has yet to be drafted, the basic idea has been for forces from Nigeria and other African countries to help Mali’s military mount a campaign against the militants. France, the United States and other countries would help with training, intelligence and logistics.

The support of Algeria, a regional power and neighbor of Mali, would be essential, diplomats say. Algeria, which waged a brutal war against militants in its own country, has one of the strongest militaries in the region and an active intelligence service. Algeria, Niger, Mali and Mauritania have set up an intelligence center in the southern Algerian city of Tamanrasset to coordinate efforts against Al Qaeda and other regional threats.

“There is a strong recognition that Algeria has to be a central part of the solution,” an American official said.

Algeria, however, has not always been supportive of an international effort in Mali, particularly since the prospect of a military campaign in Mali risked pushing militants north into Algerian territory and, in the Algerians’ estimation, radicalizing the Tuaregs, a nomadic group who live in the desert area straddling the borders of Algeria, Mali and Niger.

But as security in Mali continued to deteriorate, the Algerians have eased their objections. “There is a Malian institutional crisis,” the Algerian foreign minister, Mourad Medelci, said on Oct. 19 in an interview during an international meeting in Bamako, the capital of Mali.

“The Algerians are ready to help,” he said.

Mrs. Clinton’s visit to Algeria, her second to the country as secretary of state, followed a series of high-level meetings in Washington last week between American and Algerian officials. France’s foreign minister visited Algeria earlier this month.

In the meeting with Secretary Clinton, President Bouteflika emphasized the political side of the problem, noting steps that Algeria had taken to facilitate a dialogue between moderate Tuaregs and the Malian authorities. American officials acknowledged the value of reaching out to moderate Tuaregs, but said the United States does not want to defer the planning for a military campaign while those contacts are pursued.

“It’s very clear that a political process and our counterterrorism efforts in Mali need to work in parallel and be mutually reinforcing,” a senior State Department official said.

The Islamist gains in Mali stem from a number of factors. The fall of Col. Muammar el-Qaddafi in Libya prompted ethnic Tuareg rebels from Mali, who had been fighting alongside Colonel Qaddafi’s forces, to return to northern Mali with weapons from Libyan arsenals. They joined with Qaeda-affiliated Islamist militants who had moved to the lightly policed region from Algeria, and the two groups easily drove out the weakened Malian army in late March and early April. Then the Islamists turned on the Tuaregs, chasing them off and consolidating control in the region in May and June.

After her stop in Algeria, Mrs. Clinton traveled to Bosnia. She is also scheduled to visit Serbia, Kosovo, Croatia and Albania.