The anti-establishment 5 Star Movement (M5S) and the right-wing Lega party were arguably the main winners at Italy's election on Sunday, with both parties seeing their share of the vote grow dramatically.

Russia has courted anti-establishment parties around Europe in recent years and, having formed an allegiance to both Lega and M5S, is also expected to gain from the result. Both parties, which could have a strong say in the next Italian government, have criticized sanctions on Russia and could remove them if in power.

Lorenzo Fontana, deputy leader of Lega, told CNBC on Monday that Moscow would be pleased with the party's success. "We want to have good relations with Russia; we want to see Russia as a normal and natural partner with Europe," he said.

Asked whether Russia had congratulated Lega on its success in the election, Fontana said: "I'm sure they will be pleased with our result."

"We will see with time if we can have the relations that we wish to have with Russia, but fundamentally we wish this more for the European Union and the Italian economy," he added.

Russian President Vladimir Putin's press secretary said in his daily conference call with journalists on Tuesday that the election result was a domestic affair.

"Victory of the center-right coalition on elections is Italy's domestic affair, the sovereign right of Italian citizens to cast their votes for the political powers which they see fit for the future of their country," Dmitry Peskov said, according to remarks given to CNBC by the Kremlin's press office.

"We want Italy to remain our partner, and we hope our relations with Europe will be prosperous and will be based on the principles of mutual benefit and shared respect."