Renzi also cited the expansion of the European Central Bank's (ECB) powers following the credit crisis as another key link binding euro zone countries.
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Ahead of the ECB's most anticipated meeting for years on Thursday, where the bank's board is expected to outline plans for a quantitative easing program, he sent a clear message that he would welcome such a move.
"I respect the independence of the ECB, but I believe this is the time which they could invest in a different idea of Europe," Renzi said.
He also called for a move away from austerity-focused politics and centralized control in the euro zone, which followed the credit crisis. Cuts in bailed-out countries like Greece have been blamed for high unemployment levels, and even the rising support for extremist parties in the euro zone.
"It's finished, the time in which we work with the politics of austerity," Renzi said.
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Italy's economic situation remains precarious. Since the credit crisis, its manufacturing has fallen by a quarter, and youth unemployment is more than 40 percent, while overall unemployment is 13 percent.
That left Renzi, the former Mayor of Florence, a mammoth task when he took office last year, especially as he appears determined to serve another two years, the full term as prime minister, before calling another election. Italy has a reputation for frequent government turnover, with more than 60 administrations since the end of World War II.
Renzi's administration faces another hurdle to completing a full term -- critics say it lacks democratic legitimacy, as it was put together following a coup within his own party, rather than because the Italian people voted for him. But Renzi cited the more recent European elections, in which his Democratic Party won 41 percent of the vote, as evidence that the Italian people back him.
One of his key measures – changing the voting structure of Italy's largest "popolari", or cooperative banks, from "one shareholder, one vote" to that of most listed companies – was approved on Tuesday evening despite opposition.
This could trigger a wave of mergers in these banks, which include Banco Popolare and Monte dei Paschi di Siena. The latter famously failed euro zone stress tests last year, after its non-performing loan book grew rapidly as the Italian economy stuttered.
"The time for these reforms was 20 years ago. If my country 20 years ago had realized these reforms, we would be very happy," Renzi said. "This is not a European problem. This is our problem and we resolve this problem within our borders."
Renzi stressed the importance of increased international investment in Italy, and his plans to crack down on corruption to open up Italy beyond a narrow elite.
Even if the resulting investigations lead to MPs or powerful business people being arrested, Renzi argued that they would help restore faith in the country's laws.
"My personal goal is an open economy," he said.