Burns declined to comment on Morsi, saying only: “We’ve called on the military to avoid any politically motivated arrests.”
Several leading Republican lawmakers have already called for US aid to Egypt to be cut because of the army’s removal of Morsi.
On Monday Kenneth Roth, executive director of Human Rights Watch, urged Egyptians to be wary of recent developments.
“Dictatorship from the right can wear beards or uniforms (and a liberal-endorsed one is no better),” he tweeted.
Morsi’s supporters say his overthrow was an affront to democracy.
Before the clashes on the Oct. 6 bridge, tens of thousands of pro-Morsi protesters gathered outside Cairo’s Rabaa al-Adawiya mosque, where they have rallied for the past two weeks.