Italy's Five Star Movement welcomes support from rivals, but says it won't give up cabinet seats in any coalition deal

The Five Star Movement, known for its populist, anti-establishment and Euroskeptic rhetoric, shot to prominence in 2013, securing roughly 25 percent of the vote at the general elections even though the party had only been founded a few years before in 2009.

M5S is currently polling around 28 percent - putting them on par with the governing PD Party (Democratic Party) of Prime Minister Paolo Gentiloni and party leader Matteo Renzi. Renzi stepped down in December after losing a referendum vote on changing the electoral law — one that M5S was adamantly opposed to, throwing full weight behind the no vote.

The founder of the party, comedian turned politician, Beppe Grillo, has called for Italy leave the European bloc in the past. However, the new leader's language toward Europe is softer than his predecessor.

In an interview with CNBC over the weekend, the suited Di Maio stressed that they do not want to leave the European Union and that they would "want to sit down and have an adult conversation with other" European leaders and to work towards "re-negotiating treaties within the EU that are capping the growth of Italy, adding that a euro referendum would be a last resort measure.

"If the EU does not want to change anything, especially those regulations that are impacting our economy, then we'll ask the Italian citizens whether or not they want to remain in the euro zone. I hope the European institutions are willing to negotiate a different kind of union," he said.

Asked whether there were any parallels between the party's current plan and that of the U.K.'s David Cameron when he pushed for concessions from the EU, Di Maio emphasized that holding a euro referendum was not an election pledge so it would be wrong to compare the two situations.

Italy is set to hold a general election next year. With the current proportional representation law, no one party is projected to gain enough seats to govern with an absolute majority. Di Maio said they "are happy to receive the support of other political parties" but would not give them a representation in their government.

He also said that it depended on what type of electoral law will be in place. The two center-right parties, the Northern League led by Matteo Salvini and Forza Italia led by former Prime Minister Silvio Berlusconi (who has made a political comeback), could gather more votes than either the PD or M5S if they form an alliance.

Italy has seen a huge influx of migrants coming into the country and it has been a big topic of debate on a national level. The party is proposing three measures to address this issue: limiting the amount of migrants coming into the country, a modification of the Dublin agreement (rules on asylum), and providing more help to local councils to support the influx of people.

Di Maio went on to criticize the current Gentiloni government's handling of the crisis. He added that strategies from previous governments were to bargain the migrant situation in exchange for EU concessions.

Earlier this year, party founder Beppe Grillo expressed outrage at the government's bailout of two Italian banks saying that it amounted to a "17 billion euro gift to the banking system."

When questioned about his plans to deal with the country's ailing banking system, Di Maio said that they were not saying that "banks should not be saved," adding that the issue is with bank oversight and with some of their supervisors, including the Italian central bank governor who is about to be re-elected for a second term.