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Mrs. Clinton made a point to make Algeria her first stop on her five-day trip that will focus predominantly on the Balkans, with stops in Bosnia, Serbia and Kosovo.

The administration has been keen to work as closely as possible with Algeria, which sits between Mali and Libya.

“Obviously, against the context of what happened in northern Mali when the government forces up there collapsed and the coup happened, Algeria’s importance in this realm has become ever more important,” one senior State Department official said. “We have an awful lot at stake here, an awful lot of common interests, and there’s a strong recognition that Algeria has to be a central part of the solution.”

“Our cooperation is going to be vital in terms of the restoration of order in northern Mali and reducing the space that AQIM has to operate in and the kinds of options it has available,” the official added.

A senior American diplomat in Africa, meanwhile, told The Associated Press that 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.

The 15-nation regional bloc — the Economic Community of West African States — has discussed sending 3,000 troops to help oust the Islamist militants from northern Mali. There are, however, questions about the extent to which more troops may be needed.

U.S. officials seem wedded to the belief that a truly successful military intervention would require a major role from Algeria, whose reforms have headed off the Arab Spring tumult experienced by its neighbors and left it with the strongest military and best intelligence in the region.