The top judge of Egypt’s Constitutional Court, Adly Mahmud Mansour, has been sworn in as interim leader.
He has pledged to hold elections based on “the genuine people’s will”.
But senior figures in the Brotherhood and its political wing, the Freedom and Justice Party (FJP), were quoted as saying they would not work with the new powers – but would not take up arms or encourage followers to do so either.
The upheaval comes after days of mass rallies against Mr Morsi and the Brotherhood.
Some 50 people have died since the latest unrest began on Sunday, with correspondents saying that there are continuing fears of confrontation between the pro- and anti-Morsi blocs.
A coalition of Islamist parties – the National Coalition in Support of Legitimacy – has called for mass mobilisations to denounce the army’s actions following prayers on Friday.
Warrants
Gehad el-Haddad, a spokesman for the Muslim Brotherhood, earlier told the BBC that Mr Morsi had been put under house arrest and the “entire presidential team” was in detention.
The army said Mr Morsi, Egypt’s first freely elected leader, had “failed to meet the demands of the people”.
Mr Haddad’s father, senior Morsi aide Essam el-Haddad, and Saad al-Katatni, head of the FJP, are among those being held.
On Thursday afternoon unnamed officials said Mohammed Badie, supreme leader of the Brotherhood, had been arrested in Marsa Matrouh, a Mediterranean coastal city to the west of Cairo.
Arrest warrants have reportedly been issued for some 300 other members of the Muslim Brotherhood, including Mr Badie’s deputy, Khairat al-Shater.
Several TV stations sympathetic to the Brotherhood have been taken off the air, and a state-owned printing press is said to be refusing to print a newspaper run by the FJP.
Protesters accused the Muslim Brotherhood of pursuing an Islamist agenda and of failing to tackle Egypt’s economic problems.
Fighter jets trailing smoke drew love hearts in Cairo’s smoggy skies on Thursday in apparent celebration of the military’s role in ousting Mr Morsi’s government.
But across the city, his despondent supporters staged sit-ins in protest at what many are calling a betrayal of the democratic process.
‘Spirit of revolution’
Mr Mansour was sworn in as chief justice of the Supreme Constitutional Court on Thursday morning, then, shortly after, he took the oath to become interim head of state, vowing to “preserve the system of the republic, and respect the constitution and law, and guard the people’s interests”.
He said he would safeguard “the spirit of the revolution” which removed Hosni Mubarak from power in 2011, and would “put an end to the idea of worshipping the leader”.
He held out an apparent olive branch to the Muslim Brotherhood, saying they were “part of this people and are invited to participate in building the nation”.
Mr Mansour said fresh elections were “the only way” forward, but gave no indication of when they would be held.
The army’s roadmap for the post-Morsi era includes:
Suspension of the constitution
A civilian, transitional technocratic government
Supreme Constitutional Court to prepare for presidential and parliamentary elections
A “charter of honour” to be drawn up and followed by national media
Events in Egypt have divided international opinion, with the US, UK and UN among those expressing concern and calling for a swift return to civilian rule.
Others, such as Turkey and Tunisia, have been more forthright in their condemnation of the way Mr Morsi has been ousted.
Yet others, such as Saudi Arabia, Qatar and the United Arab Emirates – as well as Syrian President Bashar al-Assad – have welcomed the turn of events.
The recent mass protests that led to the army’s intervention were called by the Tamarod (Rebel) movement, which said it had collected a 22-million strong petition demanding Mr Morsi stand down.
Me Morsi became Egypt’s first Islamist president on 30 June 2012, after winning an election considered free and fair following the 2011 revolution that toppled Mubarak.
However his term in office was marred by constant political unrest and a sinking economy.
His moves to entrench Islamic laws and concentrate power in the hands of the Muslim Brotherhood also alienated liberals and secularists.
Source: BBC
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Egypt’s military has moved against the leadership of the Muslim Brotherhood a day after deposing President Mohammed Morsi. Mr Morsi is being detained, as well as senior figures in the Islamist group of which he is a member. Hundreds more are being sought.