With 37 percent of the vote, the centre-right alliance comprises the anti-immigrant and eurosceptic Lega party led by Matteo Salvini, while the populist Five Star Movement made the largest gains as a single party.
Italian far-right-leader Matteo Salvini said on Monday that his coalition had the "right and the duty" to govern the country after taking 37 percent of the vote in the weekend election.
"This is an extraordinary victory," the leader of the anti-immigrant Lega Nord (Northern League, or Lega) party told a press conference in Milan.
"We have the right and the duty to govern over the coming years."
The eurosceptic leader said that he would hold talks "in the coming hours" with the rest of his coalition, in particular Forza Italia party leader and former premier Silvio Berlusconi.
'Our team is ready'
Salvini said he was "committed to the deal" within the right-wing coalition that whichever party came away with the most votes would nominate the future prime minister.
"I'm not saying it has to be me, but our team is ready," he said, adding that "deals between friends are kept."
Salvini's League party largely outperformed Berlusconi's Forza Italia (Go Italy) party, taking 18 percent of the vote compared to 14 percent for the media tycoon.
The coalition is short of a majority, however, and would need to make alliances to govern.
In the election run-up, there had been talk of a potential anti-establishment alliance between the League and the populist Five Star Movement, the leading single party in the vote with 32 percent.
But when asked by journalists, Salvini ruled out the possibility.
"The team is the centre-right coalition," he said, adding that he would not form "minestrone soup" government, made up of different ingredients.
Salvini said that for eurosceptics, the results were "a step towards liberation."
Europe should fear "delinquents and parasites" rather than populist movements, he added.
He also personally thanked his ally, French far-right leader Marine Le Pen, for her "support and esteem."
Italy faces a prolonged period of political instability after voters delivered a hung parliament on Sunday, spurning traditional parties and flocking to anti-establishment and far-right groups in record numbers.
With votes counted from more than 75 percent of polling stations, it looked almost certain that none of the three main factions would be able to govern alone and there was little prospect of a return to mainstream government, creating a dilemma for the European Union.
TRT World's Sandra Gathmann has more from Rome.
Five Star Movement's support soar
A rightist alliance including former prime minister Silvio Berlusconi's Forza Italia (Go Italy!) held the biggest bloc of votes.
In a bitter personal defeat that appeared unlikely last week, the billionaire media magnate's party looked almost certain to be overtaken by its ally, the far-right League, which campaigned on a fiercely anti-migrant ticket.
But the anti-establishment Five Star Movement saw its support soar to become Italy's largest single party by far, and one of its senior officials said on Monday that forming a coalition without it would be impossible.
The League's economics chief on Monday raised the possibility of an alliance with Five Star. Any government based on that combination would be eurosceptic, likely to challenge EU budget restrictions and be little interested in further European integration.
Daniele Albertazzi, Senior Lecturer in European Politics and Postgraduate Research Director from University of Birmingham, Department of Political Science, spoke to TRT World about the election outcome.
Impact on economic recovery
Despite overseeing a modest economic recovery, the ruling centre-left coalition trailed a distant third at 22 percent, hit by widespread anger over persistent poverty, high unemployment and an influx of more than 600,000 migrants over the past four years.
Prolonged political stalemate could make heavily indebted Italy the focus of market concern in Europe, now that the threat of German instability had receded after the revival on Sunday of a grand coalition under Chancellor Angela Merkel.
In early European trading, the euro dipped while investors dumped Italian government debt, with the yield on its 10-year bonds jumping 10-basis points.
"Italy is far from having sorted its long-standing problems, and now it will have new ones. Be prepared for long and complex negotiations," said Lorenzo Codogno, a former chief economist at the Italian Treasury.
Parliament will meet for the first time on March 23 and President Sergio Mattarella is not expected to open formal talks on forming a government until early April.
Anti-establishment parties have been on the rise across Europe since the 2008 financial crisis. Italy's mainstream parties have found it especially hard to contain voter anger, with the economy still six percent smaller than a decade ago and unemployment stuck at about 11 percent.