Egypt should allow peaceful protests and discourage the infiltration of weapons at rallies, according to Alpha Oumar Konare, a former president of Mali appointed by the African Union to lead a panel on Egypt.
The official, who met deposed President Mohamed Morsi on Wednesday, told Al Jazeera that Morsi was in good health as he warned against further "derailment into violence."
"Peaceful protests form part of democracy but derailment into violence must be avoided, incitement and provocation must also be avoided, as well as arms and weapons infiltrating demonstration," he said.
Speaking about his meeting with Morsi, which follows an earlier visit by Catherine Ashton, the European Union foreign policy chief, Konare said: "We found him in good health, we a had a good, direct relaxed meeting with him."
No further details would be announced, he said, because "we are on a mission of listening to all parties - it would be premature for me to say what our conclusions would be at this stage".
Elsewhere, EU envoy Bernadino Leon was in Cairo on Wednesday to press the mediation effort, and German Foreign Minister Guido Westerwelle was due to hold talks there on Thursday.
US Republican senators John McCain and Lindsey Graham said on Wednesday that they would also visit Egypt to help quell violence and press for elections.