"This is a military coup. We will remain and deprive it of legitimacy until it is corrected," Mohamed El-Beltagy told reporters at a pro-Morsi sit-in outside a mosque in Cairo on Thursday.
Asked if the Brotherhood might take up arms, he said: "No. That is unlikely."
The 85-year-old movement, long suppressed during years of military-backed rule, renounced violence decades ago.
El-Beltagy added that the military overthrow of Morsi might push other groups, though not his own, to violent resistance.
"The issue is not with Brothers being in or out of prison. The Brothers have lived in prisons for ages," he told reporters.
"The issue now is the position of the free world that is pushing the country to a state of chaos and pushing groups other than the Brotherhood to return to the idea of change by force," he said.
Late Wednesday, General Abdel Fattah al-Sisi, the head of Egypt’s army, announced that President Morsi was no longer in office during a speech on state television.
Sisi said Morsi, who is Egypt’s first freely elected president, had “failed to meet the demands of the people.”
Following the speech by Sisi, police began arresting key presidential aides and the leaders of the Muslim Brotherhood.
Morsi’s ouster came after days of massive anti-government protests across the country.
A senior Egyptian army official said on Thursday that Morsi is being held “preventively” by the military.
“He (Morsi) is being held preventively for final preparations,” said the army official, whose name was not mentioned in the reports.
Morsi might face formal charges over accusations made by his opponents, the official stated.
The chief justice of Egypt’s Supreme Constitutional Court, Adly Mansour, has been sworn in as interim president of Egypt.