WASHINGTON — The Obama administration is debating how much more aid it can give the French military forces who are battling Islamic militants in Mali, weighing the benefit of striking a major blow to Qaeda-linked fighters in Africa against concern about being drawn into a lengthy conflict there.

The immediate issue is whether and how to supply American aerial refueling planes that would allow French jets to provide close-air support to ground forces moving north into territory held by the extremists. French and American officials have been in discussions for days, according to American and European officials, and administration officials say they expect a decision soon.

All indications are that the administration is trying to find a solution, but that any refueling would probably be approved only with restrictions.

“The discussions center on cost, and the concern about whether this becomes an open-ended mission for the French in Mali,” one Defense Department official said. “What does that mean about our commitment?”