US envoy Burns arrived in Cairo on Friday night on the heels of trips by the EU’s Middle East envoy Bernardino Leon and German Foreign Minister Guido Westerwelle.
A senior member of the Freedom and Justice Party, the Brotherhood’s political arm, said the European envoys had asked them to end their sit-ins.
Morsi supporters have also been angered by comments from US Secretary of State John Kerry, who told Pakistani television that Egypt’s military was “restoring democracy” when it ousted the Islamist leader after protests against him.
“Is it the job of the army to restore democracy?” Muslim Brotherhood spokesman Gehad al-Haddad asked in a statement on Friday.
Meanwhile, rights group Amnesty International demanded an investigation into allegations that Morsi’s supporters tortured opponents in Cairo near their protest camps.
It said opponents of the Islamist leader reported being “captured, beaten, subjected to electric shocks or stabbed by individuals loyal to the former president.”
Morsi has been formally remanded in custody on suspicion of offenses when he broke out of prison during the 2011 revolt that toppled former Egyptian president Hosni Mubarak.
Prosecutors have also referred three top Muslim Brotherhood leaders, including supreme guide Mohamed Badie, for prosecution on allegations of inciting the deaths of demonstrators.
Morsi was detained hours after the coup and is being held at an undisclosed location, where his family has been unable to see him.
EU High Representative for Foreign Affairs and Security Policy Catherine Ashton met Morsi on Tuesday and said he was “well.”