The United States is considering targeted sanctions on individuals and on entities controlled by the military.
The generals have few overseas interests, but the military's extensive business interests could suffer if foreign partners leave - as Japanese drinks company Kirin Holdings said it would on Friday.
Telenor, another company attracted to invest by Myanmar's decade of opening, said it was legally obliged to follow the order to block some social media, but "highlighted the directive's contradiction with international human rights law." US based pressure group Human Rights Watch called for the lifting of the internet restrictions, the release of detainees and an end to threats against journalists.