The Muslim Brotherhood in Egypt says it will not work with "the usurpers" after the military removed President Mohammed Morsi from power.
The statement was made on a website on Thursday after new interim leader Adli Mansour was sworn in as president.
The ABC reports Mr Mansour used his inauguration to hold out an olive branch to the Brotherhood.
"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.
However, Sheikh Abdel Rahman al-Barr - a member of the Brotherhood's executive board - dismissed the offer in a statement on the group's website.
"We reject participation in any work with the usurper authorities," the statement said.
"We call on protesters to show self-restraint and stay peaceful. We reject the oppressive, police state practices: killing, arrests, curbing media freedom and closing TV channels."
Shortly after the swearing in, the state prosecutor ordered the arrest of Muslim Brotherhood leader, Mohammed Badie and his deputy Khairat el-Shater.
The BBC says arrest warrants have reportedly been issued for some 300 other members of the Muslim Brotherhood.
Television stations sympathetic to the Brotherhood have been taken off the air by the military.
Morsi in military custody
Mr Morsi was elected a year ago. The army says he failed to meet the demands of the people.
He is in military custody and judicial authorities have began an investigation into accusations that he and 15 others insulted the judiciary.
Mr Mansour was appointed chief justice of the Supreme Constitutional Court on Tuesday.
After being sworn-in Thursday, he praised the armed forces and the Egyptian people, saying the era of "worship of the ruler" should end.
The ABC reports crowds have largely left the streets of Cairo and Tahrir Square, which saw the largest protests after the anniversary of Mr Morsi's election.
However, a coalition of Islamist parties - the National Coalition in Support of Legitimacy - has called for mass demonstrations to denounce the army's actions following Friday prayers.
The events in Egypt drew a cautious and mixed response around the world.
China said it respects the choice of the Egyptian people, while there is unease in the West about the military deposing a democratically elected leader.
Deutsche Welle Radio reports German Foreign Minister Guido Westerwelle voiced some of the strongest concerns, saying Mr Mursi's ousting was a "major setback for democracy in Egypt."
"It is urgent that Egypt return as quickly as possible to the constitutional order ... there is a real danger that the democratic transition in Egypt will be seriously damaged," he said.
The European Union said that it hoped for prompt elections in Egypt, a return to democratic rule, and the introduction of an inclusive new administration representing as broad a majority of the country as possible.
"I urge all sides to rapidly return to the democratic process, including the holding of free and fair presidential and parliamentary elections and the approval of a constitution, to be done in a fully inclusive manner, so as to permit the country to resume and complete its democratic transition," said EU foreign policy chief Catherine Ashton in a statement.
US President Barack Obama held a lengthy meeting with national security advisors in Washington after the Egyptian military moved to oust Morsi.
''We believe that ultimately the future of Egypt can only be determined by the Egyptian people," Mr Obama said in a statement.
"Nevertheless, we are deeply concerned by the decision of the Egyptian Armed Forces to remove President Morsi and suspend the Egyptian constitution."
Deutsche Welle Radio reports Mr Obama called on the military "to move quickly and responsibly to return full authority back to a democratically elected civilian government as soon as possible through an inclusive and transparent process, and to avoid any arbitrary arrests of President Morsi and his supporters."
France's foreign minister Laurent Fabius said the end goal for Egypt was still that "the people can freely choose their leaders and their future."
British Foreign Minister William Hague said that while the UK "does not support military intervention as a way to resolve disputes in a democratic system," there remained the chance for all parties to "show the leadership and vision needed to restore and renew Egypt's democratic transition."
Saudi King Abdullah sent a message to the head of Egypt's Constitutional Court, Adil Mansour, late on Wednesday to congratulate him on being named interim president.
"We pray for God to help you bear the responsibility laid upon you to achieve the ambitions of our brotherly people of Egypt," the message said.
President Bashar al-Assad of Syria was quoted by the Thawra newspaper as saying that Mr Morsi's removal from office marked "the fall of what is called political Islam."
Sudan said it was "following with concern" developments in its "sister" country Egypt.
Citing a foreign ministry statement, the SUNA news agency reported that Sudan was keen to "maintain its fraternal relations with Egypt and to enhance further the bilateral relations."