UN Secretary-General Ban Ki-moon said on Monday he was "deeply disturbed" by the deaths in custody of 37 supporters of the Muslim Brotherhood in Egypt and condemned an ambush by Islamist militants that killed 25 Egyptian policemen.
The Muslim Brotherhood supporters died on Sunday while being transferred to a prison. Government officials said they were suffocated by tear gas during an attempted escape, but the Brotherhood said the men were murdered and demanded an inquiry.
"The Secretary-General calls for a full investigation to ascertain the facts surrounding this incident," Ban's press office said in a statement.
The Egyptian policemen were on their way to their barracks in Rafah, near the border with Israel, when militants attacked them with machine-guns and rocket-propelled grenades on Monday, according to security sources.
Almost 900 people, including more than 100 soldiers and police, have been killed since the authorities forcibly dispersed Muslim Brotherhood sit-ins in Cairo on Wednesday.
"With such sharp polarization in Egyptian society, both the authorities and the political leaders share the responsibility for ending the current violence. They should spare no effort to swiftly adopt a credible plan to contain the violence and revive the political process," Ban told a news conference.
He said "the political space for the Muslim Brotherhood should be expanded, because their political space has been very limited."
He also said Egypt's democratically elected President Mohamed Morsi - who was removed from power by the army and detained on July 3 after massive protests against him - should be freed or subjected to a transparent legal process.
Ban said UN political affairs chief Jeffrey Feltman would hold discussions this week in Cairo "with a focus on how the United Nations can best support initiatives to restore peace and forge reconciliation in Egypt."
Egypt's UN Ambassador Mootaz Ahmadein Khalil on Monday told a UN Security Council debate on protection of civilians in armed conflict that the situation in Egypt was not an armed conflict and "does not threaten international peace nor security."
"It is an internal matter that would be resolved only through an Egyptian-led political process that includes all Egyptian political factions that reject violence and extremism," he said.
The Security Council, which is responsible for the maintenance of international peace and security, urged all parties in Egypt on Thursday to end the violence and exercise maximum restraint.
The 15-member council made the remarks after it was briefed on the situation in Egypt behind closed doors. Some diplomats said it was the first time in decades that the country had been the topic of a council meeting.