The leader of the Muslim Brotherhood has been arrested by Egyptian security forces in a crackdown against the Islamist movement after the army ousted the country's first democratically elected president.

President Mohamed Mursi's downfall, despite being celebrated by millions of people on Cairo's streets, created resentment among Egyptians who opposed military intervention.

An Islamist coalition led by the Brotherhood called on people across the nation to protest today in a Friday of Rejection following weekly prayers, an early test of Mr Mursi's ongoing support and how the military will deal with it.

Judge Adli Mansour used his inauguration as the new interim leader following the former president's fall from grace on Thursday to hold out an olive branch to the Brotherhood, Mr Mursi's power base.

"The Muslim Brotherhood are part of this people and are invited to participate in building the nation as nobody will be excluded, and if they respond to the invitation, they will be welcomed," he said.

The air force staged a series of flypasts involving dozens of planes over Cairo to highlight its role in helping to oust Mr Mursi.

It came as a Brotherhood official said it would not work with "the usurper authorities". Another of its politicians said Mr Mursi's overthrow would push other groups, though not his own, to violent resistance.

Mr Mursi's removal after a year in office marked another twist in the turmoil that has gripped the Arab world's most populous country in the two years since the fall of Hosni Mubarak.

In London, Foreign Secretary William Hague called for a swift return to democracy after speaking to Egypt's foreign minister who assured him of early elections for a successor to Mr Mursi.

He said: "It is the problem with a military intervention, of course, that it is a precedent for the future. If this can happen to one elected president, it can happen to another

"That's why it is so important to entrench democratic institutions and for political leaders – for all their sakes and the sake of their country – to find the compromises they haven't been able to make in Egypt over the last year."

Mr Hague stressed the need for the early release of political leaders and journalists currently in detention ahead of new elections.

He added: "I have made the point that we regard it – and many other countries will regard it – as important those elections are totally free and fair and that everyone is able to compete in them."

"In the long run it is democratic institutions that bring stability."

Across the Middle East, governments reacted to Mr Mursi's fall in ways that reflected their embrace or loathing of political Islam.

"Military intervention is totally unacceptable," said President Moncef Marzouki of Tunisia. The country's ruling Islamist party, Ennahda, condemned what it called a "coup against legitimacy".

Turkey's Foreign Minister Ahmet Davutoglu said: "It is unacceptable for a government that has come to power through democratic elections to be toppled through illicit means and, even more, a military coup."

The president of the United Arab Emirates, Sheikh Khalifa bin Zayed al-Nahayan, spoke of his "consideration and satisfaction" in a cable to Mr Mansour.

US President Barack Obama, whose administration provides $1.3 billion a year to the Egyptian military, expressed concern about Mr Mursi's removal and called for a swift return to a democratically elected civilian government.

Nato Secretary-General Anders Fogh Rasmussen said he was gravely concerned about the situation. But the new emir in Qatar, which has provided billions of dollars in aid to Egypt following the ousting of Mubarak, congratulated Mr Mansour on his appointment.