The publication of the cartoons in Danish and other European newspapers, including one showing an image of the prophet with a bomb for a turban and another showing him wielding a knife, provoked a storm of criticism from Muslims.
Javier Solana told reporters in Cairo on Tuesday: "We have constructed a very deep relationship and we would like not only to maintain that but to deepen that relationship.
"We should not allow the latest developments to separate us."
He arrived from Saudi Arabia, where he held talks with the head of the Organisation of the Islamic Conference.
The group is lobbying for the United Nations to include language against blasphemy in the tenets of a new human rights body.
"We are working on some ideas. I cannot be very precise, but we are working on some ideas that maybe it is possible to get through," Solana said, when asked about such proposals.
"Our societies should cement a sense of dialogue, a sense of having relations guided by respect, by affection, by the number of problems that we have to solve together," Solana said after talks with Hosni Mubarak, Egypt's president.
Solana has noted the concerns of
Muhammad Tantawi (R)
Solana said one of the main reasons for his visit to Egypt was "a profound desire ... to rebuild bridges between Europe and the Muslim world".
Solana also met Muhammad Sayed Tantawi, the shaikh of al-Azhar, one of the oldest and most revered seats of Islamic learning.
After those talks, Solana said: "He has made his comments of a conceptual nature and I said I would take good note of the things he has said."
Though Muslims consider any portrayal of Prophet Muhammad blasphemous, many people in Europe have supported the freedom of the press to publish the cartoons.