Hasina had sought to quell nationwide protests against her government since early July but she fled the country after nearly 100 people were killed on Sunday.
Miller said that the United States had seen reports that the army refused pressure to crack down further on student-led demonstrations.
“If it is true in fact that the army resisted calls to crack down on lawful protesters, that would be a positive development,” he said.
“We welcome the announcement of an interim government and urge any transition be conducted in accordance with Bangladesh’s laws,” he said.
Asked if the military should choose the next leadership, Miller said, “We want to see the Bangladeshi people decide the future Bangladeshi government.”
He said that the United States also was “deeply saddened about the reports of human rights abuses, casualties and injuries over the weekend and past weeks.”
“It is vital that we have full and transparent investigations to ensure accountability for these deaths,” Miller said.