(CNN) -- Egypt's factions must find a way to bridge their differences and pave the way for a political solution that involves all sides if the country is to leave its current chaos behind, the European Union's top diplomat said Tuesday.
"Only an inclusive process will work," EU High Commissioner for Foreign Affairs Catherine Ashton told reporters Tuesday after visiting with the country's deposed president, current leaders, Muslim Brotherhood members and others during a brief trip.
"And though I recognize that is challenging, it is really important to begin now," she said.
Egypt has suffered from sporadic violence since the July 3 military coup that removed President Mohamed Morsy from power on the heels of mass protests against his rule. He is being held at an undisclosed military facility on a variety of criminal charges.
Most recently, violent clashes between security forces and protesters in Cairo on Saturday left dozens of Morsy supporters dead, and officials have threatened to disband a sit-in of the former president's supporters -- an act that could spur yet more bloodshed.
Several Egyptian human rights groups demanded in a statement released Tuesday that Interior Minister Mohamed Ibrahim resign over the Saturday incident and demanded that government forces refrain from further violence.
"The Egyptian security forces' recurrent use of excessive, lethal violence in the face of political protest will only exacerbate the political ills that led Egyptian society to rebel against the policies of Mubarak, the Supreme Council of the Armed Forces (SCAF), and the Muslim Brotherhood," according to the statement, which was signed by 10 human rights, womens' and legal organizations.
Speaking at a news conference with Ashton, Vice President Mohamed ElBaradei said he agrees with Ashton's call for a non-violent approach that includes the Muslim Brotherhood and other groups in a political solution.
"I want to emphasize again that our immediate priority, as we shared with Lady Ashton, is to stop violence in all its forms and shapes and try every possible way to find a peaceful solution," he told reporters. "Violence is not a solution. It opens new wounds. It doesn't heal old wounds."
Muslim Brotherhood officials said on the group's website that they will continue protesting until Morsy is restored to office.
Speaking to the possibility that security forces could clear a Cairo square where some Morsy supporters are staging a sit-in, ElBaradei said preparation must proceed for both a political resolution and one in which security forces are called in to end the situation.
"The political resolution has the priority, and I wish there will be political resolution before the security one," he said.
Ashton, who has previously criticized Morsy's forced ouster, said in an earlier interview with CNN that Egyptian officials should release political prisoners and that all sides should rein in violence.
But, in the news conference, ElBaradei noted Morsy is facing charges, echoing Prime Minister Hazem El-Beblawi's statement Monday that the former president should continue to be held.
Ashton, who met with Morsy for two hours Monday, said Morsy is well. He is keeping up with current events through newspapers and television, she said.
Ashton -- the first high-level official outside the Egyptian military to meet with the former president since the military whisked him away this month -- said she was kept in the dark about his location during their meeting. "I don't know where he was," she told journalists in Cairo.
She had insisted with the interim government that she be allowed to meet with Morsy as a precondition to her visit to Cairo. "And that was freely offered to me," she said.
Though she had a "friendly and open and very frank discussion," she did not pass on details. She told Morsy that she would not represent his views to the world.
"He cannot correct me, if I do it wrong," she said.
During her trip, she also met with acting President Adly Mansour and Gen. Abdel Fattah al-Sisi, who led the military coup against Morsy.
"We are not here to impose. The people of Egypt will determine their own future," Ashton said. But she expected Egypt's leaders to ensure that happens.
Morsy's party did not meet with Ashton, but it let her know it is sticking by its demands.
"We made it clear to her that we will keep protesting for our civil rights until the legitimate president is released," said Essam Elerian, the vice chairman of the Freedom and Justice Party.
"And as we said it before, restoring the democratic legitimacy of our elected president is non-negotiable."