Italy have been drawn alongside England, who they face in their opening game in Manaus on June 14, Uruguay and Costa Rica in what is arguably the toughest group of the competition.
The four-time winners failed to get into the knockout stages in South Africa four years ago, but responded well by reaching the final of the 2012 UEFA European Championships.
Milan midfielder Montolivo is well aware of the challenge facing Cesare Prandelli's men in Brazil and expects the group to be settled by the finest of margins.
"Certainly it is not going to be easy," said in an interview with Forza Milan magazine.
"The most delicate game is always the first - we take to the field against England, a direct competitor for passage to the next round.
"In a group of four it could happen that we will finish on level points, and the difference could precisely be in the direct clashes.
"For us it is therefore important to start well. England and Uruguay are two tough teams to face - in my opinion, in the fight for the title immediately after the favourites Spain, Brazil and Germany.
"Then, do not underestimate Costa Rica, an unpredictable outsider, very strong from a physical point of view.
"Who could be the surprise of the World Cup? I hope that the main surprise might just be Italy, who do not start as favourites from the view of predictions."
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