Renzi was speaking after hosting Egyptian President Abdel Fattah al-Sisi on the opening day of a trip to Italy and France that marks the former general's first official visit to Europe since his 2013 overthrow of his elected Islamist predecessor Mohamed Morsi.
"Italy is absolutely convinced that the Mediterranean is not the frontier but the heart of Europe and Egypt must be considered a strategic partner in addressing together the problems of this area," Renzi said.
"The only way to avoid an escalation of them is through very strong cooperation between Egypt and Europe."
Renzi announced he would be sending a major trade delegation to Cairo in February in an effort to boost the two countries' economic ties and also said there would be annual high-level meetings to address issues of mutual concern.
Chief among these is the descent of Egypt's neighbour Libya into chaos which has contributed to a surge in the number of refugees arriving in Italy by boat.
Sisi echoed Renzi's comments, making it clear he expected help rebuilding Egypt's shattered economy in return for his country helping to combat Islamic
militancy - a role which has led to Western governments largely dropping their objections over the way the president came to power and his crackdown on dissent.
"We expect a real reaction," Sisi said. "Real support from Europe for Egypt in the upcoming period."
'The problem of Libya'
Both leaders called on the international community to refocus their attention on the disintegration of Libya into a collection of warring Islamist fiefdoms.
"Ukraine, Syria, Ebola - these questions are very important but we also have to address the problem of Libya," the Italian premier said.
Sisi said Egypt's priority was a stable Libya and urged the international community to back up government forces there.
"The price of intervention in Libya should not be the division of Libya," he said.
Sisi also pledged to enact legislation to make it easier to invest in Egypt. "The procedures have been very long in the past and we are working on the bureaucracy," he said.
Renzi also said international organisations had to be more sympathetic to Egypt's plight in dealing with the spillover from the unstable countries surrounding it.
"We have had 150,000 refugees or asylum seekers arrive in Italy this year, which is a record number. But Egypt has five million at the moment. That needs to be said loudly."
Sisi's record on rights and democracy did not appear to have come up in the meeting with Renzi, but it was highlighted earlier in the day by Pope Francis, who urged the Egyptian leader to strengthen constitutional safeguards on human rights and religious freedom, according to Vatican officials.
Sisi's visit was celebrated by hundreds of Egyptian supporters in Rome's city centre, where they danced draped in the national flag to music at a street party, holding up banners with the president's face.