Morsi himself has been formally remanded in custody on suspicion of offences committed when he escaped from prison during the 2011 revolt that toppled former president Hosni Mubarak.
US Senators John McCain and Lindsay Graham are expected in Egypt for a series of talks on Tuesday, in a fresh push for a solution.
In Cairo, hundreds of Morsi loyalists marched to the High Court, calling for the release and reinstatement of their leader, blocking traffic in the centre of the capital.
Supporters of Morsi Egypt’s first freely elected president see his ouster by the military as a violation of democracy and insist on nothing short of reinstatement.
The interim leaders however say there is no turning back on the army drafted roadmap announced after Morsi’s ousting on July 3 and which provides for new elections in 2014.
Both the interior ministry and the army have repeatedly called on pro Morsi protesters to lift their sit-ins which have paralysed parts of the capital and increased divisions in the country.
Authorities have promised Morsi loyalists a safe exit and said an end to their protests would allow the Muslim Brotherhood to return to political life.
Days of heated diplomatic activity in Cairo have seen visits by Burns, EU foreign policy chief Catherine Ashton, Arab diplomats and an African Union delegation.
On Sunday, Sisi met Islamist leaders to try to mediate a solution with Morsi supporters.
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