CAIRO (AFP) - European Union foreign policy chief Catherine Ashton flew into Egypt for talks on 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.

Even after the deaths of 72 people at a pro-Mursi demonstration in Cairo on Saturday, supporters of the ousted president remained defiant, saying they were determined to maintain what they insisted were peaceful protests. Nine more people died in violence in Egypt's second city, Alexandria.

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

Mr ElBaradei on Saturday night denounced the "excessive use of force" against protesters.

State news agency MENA said Ms Ashton would also hold talks with members of deposed president Mohamed Mursi's Muslim Brotherhood and the Tamarod group that organised the huge protests that led up to his overthrow by the army.

"I deeply deplore the loss of life," said Ms 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".

UN leader 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.

Mr 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", Ms Song added.

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

Egypt's presidency reacted on 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 Mohamed 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.

And the National Defence 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.

The council, presided over by Mansour, includes the army chief as well as the prime minister and interior minister.

Mursi loyalists, still camped out at the scene of Saturday's violence, were defiant.

"There are feelings of agony and anger, but also a very strong feeling of determination," Brotherhood spokesman Gehad el-Haddad told AFP.

Mr Mursi's supporters said they were targeted with live fire, while the interior ministry insisted only tear gas had been used.

Saturday's violence, which came after a night of rival protests for and against Mr Mursi, was the bloodiest incident since the Islamist leader was forced from power and detained by the army on July 3.

Sporadic violence continued on Sunday, with a security source reporting three people killed in clashes between Mursi supporters and opponents in Port Said and northern Kafr El-Zayat.

In Rafah meanwhile, an attack on a military post near the border with the Palestinian-controlled Gaza Strip left one soldier dead and eight wounded overnight Sunday to Monday.

Saturday's violence prompted international concern, including from US Secretary of State John Kerry, who called on authorities to "respect the right of peaceful assembly and freedom of expression".

US Democratic Senator Dianne Feinstein said her government should "relook at granting aid" to Egypt.

But Egypt's National Salvation Front - a liberal and leftist grouping - said Morsi's supporters bore some blame for their "provocative approach".

The violence came after army chief General Abdel Fattah al-Sisi, who led the coup that ousted Mursi, called for demonstrations to support a crackdown on "terrorism".

Mr Mursi, who was elected after a 2011 uprising, has not been seen since his July 3 ouster.

He is being held on accusations related to his escape from prison during the protests that overthrew former president Hosni Mubarak.