"Relations between Russia and Italy have a wide scope, from the fight against terrorism to environmental problems. We hope this co-operation will further develop in all areas," said Ivanov.
The Russian minister recalled that at his meeting with Frattini, Russian President Vladimir Putin emphasised the importance of relations with Italy.
Ivanov said the Russian head of state and Italian Prime Minister Silvio Berlusconi met six times in the past year.
Frattini in turn noted that Europe intended to consolidate interaction with Russia.
"The recent measures linked to the fight against terrorism show the direction of our co-operation," said Frattini.
Italy is convinced that security and stability in Europe are impossible without active co-operation with Russia, and the first signs of it can already be seen, said Frattini.
The Italian foreign minister described the relations between the EU and Russia as strategic partnership.