* League leader says party has right to govern
* Anti-establishment 5-Star also claims leadership role
* Long period of political stalemate forecast
* Italian assets under pressure (Adds 5-Star's Di Maio comments)
ROME, March 5 (Reuters) - Two anti-establishment leaders made early plays to govern Italy on Monday, sending ripples across the euro zone after voters relegated mainstream parties to the sidelines in delivering a hung parliament.
With the bloc's third-largest economy seemingly facing prolonged political instability, the anti-immigrant League claimed the right to rule after its centre-right alliance won the largest bloc of votes.
"We have the right and duty to govern," its leader Matteo Salvini told a news conference, saying investors should have no fear of it taking office as shares, bonds and the euro weakened on prospects of a eurosceptic-led administration promising to ramp up spending.
Minutes later, the head of the biggest single party, the anti-establishment 5-Star Movement, said it was ready to take on a responsible leadership role.
"We're open to talk to all the political forces," 31-year-old Luigi Di Maio said in a statement. "We feel the responsibility to give Italy a government (as)... a political force that represents the entire nation."
With the vote count well advanced and full results due later on Monday, it looked almost certain that none of the three main factions would be able to govern alone, and President Sergio Mattarella is not expected to open formal coalition talks until early April.
In Brussels, a European Commission spokesman said it was confident a stable administration could be formed, "and in the meantime Italy has a government with whom we are working closely."
Salvini criticised both the euro and European Union restrictions on national budgets. "The euro was, is and remains a mistake," he said, but added that a referendum over Italy's continued participation in the single currency was "unthinkable".
The rightist alliance that also includes former prime minister Silvio Berlusconi's Forza Italia (Go Italy!) was on course for around 37 percent of the vote - but for the first time the League emerged as the senior partner.
The role reversal marks a bitter personal defeat for the billionaire media magnate and his party, which took more moderate positions on the euro and immigration while the far-right League campaigned on a fiercely anti-migrant ticket.
Salvini said that, while not interested in a broad "minestrone" coalition, the League would be willing to talk to all parties.
Earlier on Monday, its economics chief Claudio Borghi raised the prospect of an alliance with 5-Star - heading for some 32 percent of the vote - which would likely be little interested in further European integration.
Anti-establishment parties have been on the rise across Europe since the 2008 financial crisis.
In Italy, where the economy is 6 percent smaller than a decade ago and unemployment is stuck near 11 percent, Sunday's biggest loser was the party that has ruled since 2013.
Despite overseeing a modest recovery, the Democratic Party's centre-left coalition trailed on 22 percent, also a victim of widespread anger over an influx of more than 600,000 migrants over the past four years.
Its leader, former prime minister Matteo Renzi, will speak publicly at 5 p.m. (1600 GMT), a spokesman said, with speculation swirling that he will resign.
New elections to try to break the deadlock are another plausible scenario.
A prolonged stalemate could make heavily indebted Italy the focus of market concern in Europe, with the threat of German instability receding after the revival on Sunday of a grand coalition under Chancellor Angela Merkel.
In early afternoon trading, Italian stocks fell 1 percent, Italian government bonds sold off and the euro was under pressure.
During two months of election campaigning, party leaders repeatedly ruled out post-election tie-ups. However, Italy has a long history of finding a way out of political logjams.
Having once rejected talk of any power sharing, 5-Star now says it is willing to discuss common policies but not negotiate over cabinet posts.
Formed in 2009, it has fed off public fury over institutional corruption and economic hardship. Some have questioned whether other parties would be able to work with it.
"Di Maio wins, Italy ungovernable," was the front page headline in La Stampa newspaper.
Having ditched earlier ambitions to quit the euro, 5-Star's flagship proposal in the election campaign was a minimum monthly income of up to 780 euros ($963) for the poor, helping it draw massive support in the underdeveloped south.
By contrast, Salvini and Berlusconi - heading for almost 18 percent and 14 percent respectively - appeared to have dominated the wealthier north, with the centre-left squeezed into a narrow stretch of central Italy.
"It's what we expected, political deadlock. A government is needed," Rome resident Giuseppe Bruni told Reuters. "We are in the hands of the president and the willingness of political parties to put a government together."
($1 = 0.8097 euros)
(Additional reporting by Gavin Jones, Francesca Piscioneri, Giselda Vagnoni and Isla Binnie; writing by John Stonestreet; editing by Steve Scherer)