The US embassy in Egypt denied claims by the Muslim Brotherhood that a protest was held outside the US consulate in Alexandria – Egypt's second city – on Monday.

"The US Embassy confirms that the reported 15 July protests in front of the US Consulate in Alexandria did not indeed take place," the embassy told Ahram Online.

The Muslim Brotherhood's spokesman in Alexandria Anas El-Qadi was quoted by the Brotherhood's official website Ikhwanonline as saying that the group's "protest in front of the US consulate is aimed against the real leaders of the coup d'etat."

The Muslim Brotherhood, from which Morsi hails, has rejected the popularly-backed military overthrow of the elected president on 3 July and has since been staging protests – while maintaining a mass sit-in in Cairo – to demand his reinstatement.

US Deputy Secretary of State William Burns visited Cairo on Monday and praised the army for "responding to Egyptians' will" during a meeting with Egypt's defence minister Abdel-Fattah El-Sisi.

El-Sisi announced the removal of Morsi and a transitional phase of at least six months on 3 July, following nationwide protests demanding the resignation of the Islamist president. Morsi's whereabouts remain unknown, but the army said in an earlier statement that he was being held "for his own safety."

The Muslim Brotherhood and its Islamist allies have staged several mass marches around Cairo and in a number of governorates to press for Morsi's reinstatement. Violent clashes erupted during pro-Morsi demonstrations in the districts of Giza and Ramsis on Monday night and continued into the early hours of Tuesday.