An intensifying dispute between Italy and the European Union hit financial markets on Tuesday, with investors bracing for another budget showdown between Rome and Brussels.

European stocks and the euro were both trading lower during afternoon deals, following reports the euro zone's third-largest economy could soon face disciplinary steps from the EU's guardian of healthy public finances.

Italy's Deputy Prime Minister Matteo Salvini said Tuesday that Rome could be hit with a fine of 3 billion euros ($3.4 billion) for accumulating debt and deficits that break EU rules.

Speaking shortly after his anti-immigration Lega party triumphed in European elections, Salvini said he would use of all his energy to fight what he claimed were outdated and unfair European fiscal rules.

European Commission Vice President Valdis Dombrovskis told CNBC's Silvia Amaro on Tuesday that he could not confirm whether Italy would be slapped with a hefty fine.

But, he said the EU's executive arm — the European Commission — did have "some concerns" about Italy's fiscal trajectory.

In the event of a fine, the sanction would require the approval of EU finance ministers.