Speaking at a joint news conference with leader Aung San Suu Kyi in Myanmar's capital, Tillerson said the United States would consider individual sanctions against people found responsible for the violence, but he would not advise "broad-based economic sanctions" against the entire country.
While the army insists it has only targeted Rohingya rebels, refugees massing in grim Bangladeshi camps have described chilling and consistent accounts of widespread murder, rape and arson at the hands of security forces and Buddhist mobs. "I have a hard time seeing how (broad-based sanctions) help this crisis".
A Nobel Peace Prize victor, Ms Suu Kyi has come under fire from the global community over her handling of the crisis. Myanmar is predominately Buddhist and Rohingya people do not have citizenship and the government considers them as illegal migrants from Bangladesh.
MYANMAR will allow the return of Rohingya Muslims to their homes, President Rodrigo Duterte's spokesman said on Monday.
"Once again, Myanmar's military is trying to sweep serious violations against the Rohingya under the carpet", it said. "You can't just impose sanctions and say therefore the crisis is over".
"The scenes of what occurred out there are just horrific", he added.
But her statement failed to stop the criticism as the exodus of refugees continued along with violence. At Wednesday's news conference Suu Kyi denied she had been silent on the issue, saying she had personally commented on the situation as well as issued statements through her office.
"I don't know why people say that I've been silent". The military is in charge of the operations in northern Rakhine, and ending them is not up to Ms Suu Kyi.
She said her comments on the issue were not "interesting enough" or "exciting" but "meant to be accurate". The military has more representatives even in parliament there (than her party has).
While the report acknowledged that battles against militants from the Arakan Rohingya Salvation Army had left 376 "terrorists" dead, it also claimed security forces had "never shot at the innocent Bengalis" and "there was no death of innocent people".
This week the Burmese military published the results of an internal investigation clearing its forces of shooting villagers and of a campaign of sexual violence.
Rights groups blasted the report as an attempt to "whitewash" atrocities by a military with a long history of abuses, especially against ethnic minorities in border regions.