Zarif's comments came after talks with Federica Mogherini, the current Italian foreign minister who will shortly take over from Britain's Catherine Ashton as the public face of EU relations with the rest of the world.
Zarif said the crisis in Iraq and Syria demonstrated that the EU and Iran need to work together to address common challenges.
"The same challenges (Iran faces) are before the EU, both as international security and local and domestic security.
"The very sad fact a very large number of foreign fighters are now in Iraq and Syria brings this issue very close to home here in Europe.
"So I think we have common ground both in terms of opportunities for great cooperation, greater economic development, dialogue on human rights as well as cooperation to address these common challenges.
"This mixture… should provide us with a basis for better work together particularly with the role Italy has played as a bridge between Europe and the Islamic world. That role can be further enhanced by the role Mrs Mogherini will play as the High Representative of Europe."
Mogherini's first major goal in her new job will be to wrap up a deal with Iran on the Islamic state's contested nuclear programme, for which a November deadline has been said.
The Italian minister said her discussions with Zarif had left her hopeful that could be achieved.
"We have said that an agreement ought to be reached by November in order to guarantee greater stability in the region," Mogherini said.
"It is my hope the negotiations will have a positive outcome and that this will be done by November 23rd, the agreed deadline.
"I was assured that there is a strong political will in Tehran for this to happen and we hope that there will also be the necessary technical steps taken."
Mogherini said Italian officials had been in close discussions with their Iranian counterparts on how to bring stability to Iraq/Syria.
"We share a belief in the need to respond with a military presence in the emergency situation we are in but above all we believe in the need for an inclusive government in Baghdad," Mogherini said.