(CNN) -- U.S. Defense Secretary Chuck Hagel urged an inclusive political process to his Egyptian counterpart Saturday, one day after supporters of Egypt's deposed President Mohamed Morsy violently tried to storm a media compound, officials said.
Hagel expressed concern about the violence between the Morsy supporters and Egypt's security forces, in which at least 31 people were arrested in the Media Production City clash.
Egyptian Defense Minister Gen. Abdel Fattah al-Sisi assured Hagel that the new military-backed government was working toward political reconciliation and remained committed to a political road map leading to elections and the formation of a constitution, Pentagon spokesman George Little said.
Friday's clash came as the new military-backed government called for an end to two massive pro-Morsy sit-ins in Cairo that have drawn tens of thousands of protesters -- primarily Muslim Brotherhood supporters -- since the military ousted Morsy from office a month ago.
Egyptian Foreign Minister Nabil Fahmy reiterated Saturday that any action against the Muslim Brotherhood sit-in would "take place within the framework of the law."
Fahmy also said he met with U.S. Deputy Secretary William Burns on Saturday and added he spoke by phone with U.S. Secretary of State John Kerry about the country's violence.
"There are people who are getting more and more frustrated with the ongoing tensions that exist and the ongoing breakdown in security, and they feel to a large degree correctly that this is caused by the Islamist threat, specifically the Muslim Brotherhood," Fahmy said.
As dusk fell Friday, cameras captured how packed the streets were in Cairo's Rabaa al-Adawiya and Nahda Masr squares as people shouted and waved flags. Egyptian state TV reported that security forces would cordon off the squares so people could only exit and not enter.
"The security problem goes beyond Rabaa. That's why it's important to initiate the reconciliation process by ending the violence," Fahmy said. "Some indication that these violent acts have stopped -- that will help open the door for a dialogue on how to get them to participate in the process."
Fahmy also met Saturday with Bernardino Leon, the European Union's special representative for the southern Mediterranean, Egyptian officials said.
Fahmy apprised the two diplomats -- Burns and Leon -- of the new government's commitment to national reconciliation with all political forces, as long as they refrain from violence or inciting it, a foreign ministry spokesman said.
While Fahmy was open to opinions from foreign delegations, he told the diplomats that domestic issues lie with the Egyptian government, the spokesman said.
"It is with a sense of confidence that we receive emissaries from different countries, those who we agree with and those who we may not agree with," Fahmy said. "We will listen to their point of view. If they are helpful, we will take them into account and move forward with them. If not, we will listen politely and not implement them."
Burns and Leon agreed that Egypt's future will be decided by Egyptians without foreign intervention and told Fahmy their "visits are aimed at hearing the views of the government and all of the political forces, and at providing any assistance possible to end the current state of polarization," according to a statement by the Egyptian Foreign Ministry.
They also told Fahmy that ending the violence and achieving national reconciliation are "necessary in order for Egypt to overcome the momentous challenges it faces, especially the economic challenges and the need to return tourism to its normal rates," the Egyptian statement said.
Morsy supporters have vowed not to end the protests until Morsy is returned to office, and they have been gearing up in recent days for a possible confrontation with the military after the government's warning.
As tensions rise across the country, so do fears of possible further violence in a country facing its worst crisis since the popular uprising that toppled Hosni Mubarak in 2011. Hundreds have been killed and thousands more wounded in clashes between Morsy's supporters and those opposed to his rule.
Burns and Leon also met with Morsy supporters on Saturday.
"Our view of legitimacy is constitutional legitimacy," Tarek El-Malt, spokesman of the pro-Morsy Anti-Coup Coalition, told Burns and Leon.
But this doesn't mean the protesters' top demand of reinstating Morsy has been sidelined, El-Malt told CNN.
"We don't respect the coup and reject it, but we respect the people that protested on June 30," when anti-Morsy protesters demanded he step down, he added.
Solutions, he said, must respect the demands of the anti-Morsy protesters from June 30 and those of the pro-Morsy activists who have camped out in the streets since the coup calling for Morsy's reinstatement.
The Egyptian Interior Ministry said it is aware that some pro-Morsy activists "are afraid of being pursued by security forces or by threats from the organizers of these gatherings" if those activists want to go home, according to a ministry statement.
"We affirm our promise to protect them and guarantee their safety," the Interior Ministry statement said.
"Their continued presence in those areas, however, will make them legally responsible should they get involved in illegal activities," the ministry said. "This comes after evidence showed that the organizers of those protests were proven to have committed murder, torture, kidnapping, possess weapons, blocking the roads, incitement, hate crimes, demeaning of religions, destructions of property and endangering the lives of residents."
The ministry also charged that the protesters "were brain washed by the organizers" and "have been hijacked by the Muslim Brotherhood in order to keep them under their control," the statement said.
"In so doing the Muslim Brotherhood is attempting to exploit them to leverage its political and private gains," the ministry said.
CNN's Ali Younes in Atlanta and Sarah El Sirgany in Cairo contributed to this report.