was sworn into office on Thursday, met with army chief and Defence Minister General Abdel-Fattah el-Sissi as well as Interior Minister Mohammed Ibrahim, who is in charge of the police, at the Ittihadiya presidential palace.
He also met with his new aides -- constitutional consultant Judge Aly Awad Saleh, political consultant Mustafa Hegazy, and security consultant General Rafaat Shehata.
According to a presidential source, the meetings focused on ways to secure protests and ensure national security.
The source said that Adly focused his discussion with constitutional and political aides on a new constitutional declaration that will be announced soon. The declaration will provide details on how the upcoming transitional period will be managed.
Adly will also meet with representatives of different political forces and members of the Rebel movement.
Meanwhile, a tense calm has descended on Egypt following a night of fierce clashes between supporters and opponents of Morsi.
Tens of thousands of angry supporters of 61-year-old ousted president, chanting slogans like "down with military rule", took to the streets after Friday prayers demanding his reinstatement.
At least 36 people were killed and more than 1,000 wounded in the violence.
In the capital, the protesters holding images of Morsi marched towards the Republican Guards Club, where Morsi is believed to have been put "under guard" since Wednesday night.
Despite warning from soldiers, the crowd tried to storm the Guards headquarters, prompting the soldiers to open fire - first into the air, then at the demonstrators, killing four demonstrators and wounding dozens, local media reported.
In running street battles in Cairo, more people were dead, including two at iconic Tahrir Sqaure, and scores of others injured, reports said.
The worst hit was coastal city of Alexandria, the second largest city in Egypt, where street fighting and clashes left 12 people dead, mostly from gunshot wounds.
Meanwhile, Brotherhood-led National Alliance in Support of Electoral Legitimacy today vowed more protests in support of the deposed president.