EU Foreign Policy Chief Catherine Ashton flew into Egypt for talks Monday as international pressure increased on the new regime over the weekend’s violence, which claimed more than 80 lives.

EU Foreign Policy Chief Catherine Ashton flew into Egypt for talks Monday as international pressure increased on the new regime over the weekend's violence, which claimed more than 80 lives.

But the country's new rulers warned they would take "decisive and firm" action against protesters if they went beyond their right to peaceful demonstration.

Egypt's vice presidency said Ashton would meet with interim president Adly Mansour and Mohamed El-Baradei, who is vice president for international affairs.

El-Baradei had denounced on Saturday night what he considered was the "excessive use of force" against protesters.

State news agency MENA said Ashton would also hold talks with members of deposed President Mohammad Mursi's Muslim Brotherhood and the Tamarod group that organized the huge protests that led up to his overthrow by the Army.

“I deeply deplore the loss of life," said Ashton in a statement, adding that she would be pressing the need for all sides to be included in the return to democracy, including the Muslim Brotherhood".

For his part, UN Secretary General Ban Ki-moon warned Egypt's interim leadership on Sunday that every death made it harder to drag the country out of its crisis, a spokeswoman said.

Ban "expressed his profound concern about the direction in which the transition in Egypt is moving" and condemned the heightened violence, UN spokeswoman Morana Song said.

He called on the authorities to protect "all Egyptians, regardless of party affiliation", Song added.

But tensions remained high after Saturday's killings, the bloodiest incident since Mursi's overthrow on July 3.

Egypt's presidency reacted Sunday to the bloodshed a day earlier.

"We are saddened by the spilling of blood on the 27th," Mansour adviser Moustafa Hegazy told reporters.

But he dubbed the protest area where the deaths occurred a "terror-originating spot" and said "we cannot decouple this from context of terrorism".

Interior Minister Mohammad Ibrahim warned that his forces would "not allow any mercenary or person bearing a grudge to try to disrupt the atmosphere of unity.

“We will confront them with the greatest of force and firmness," he added.

In parallel, the National Defense Council warned protesters on Sunday night "not to exceed their rights to peaceful, responsible expression of their opinions".

They would face "decisive and firm decisions and actions in response to any violations", the statement warned.

Mursi supporters call for new protests

Despite threats, supporters of Mursi called for new protests on Monday, as Ashton held talks with the government and opposition.

The “Anti-Coup Alliance of Islamist groups” organizing protests against the ouster of President Mohammad Mursi urged demonstrators to march on security buildings on Monday night and called a million-man march for Tuesday.

“We... call for a million person march under the banner of 'Martyrs of the Coup' on Tuesday," the alliance said in a statement.

It further urged Egyptians "to go out into the streets and squares, to regain their freedom and dignity -- that are being usurped by the bloody coup -- and for the rights of the martyrs assassinated by its bullets.”

It also called for protesters to march on security buildings across Egypt on Monday night "to condemn the criminal acts and the firing of live ammunition by the interior ministry at peaceful demonstrators."