* Emphatic win gives prime minister almost 41 percent of vote
* PM Renzi says he has mandate to make his mark in Europe
* Says Italy can now accelerate reforms
* Grillo challenge fades after bitter campaign (Adds quotes, detail, early results from local elections)
By Steve Scherer and James Mackenzie
ROME, May 26 (Reuters) - Italian Prime Minister Matteo Renzi promised on Monday to push economic and institutional reforms in Rome and promote his pro-growth agenda in Brussels after securing an emphatic victory in elections for the European parliament at the weekend.
In the final tally, more than 40.8 percent of Italian voters cast ballots for Renzi's centre-left Democratic Party (PD), almost double the 21.2 percent won by the anti-establishment 5-Star Movement of former comic Beppe Grillo.
Former premier Silvio Berlusconi's Forza Italia party came in third with just 16.8 percent of the vote. Initial results from local elections also pointed to strong wins for the PD in two regional ballots and more than 4,000 town councils.
Sunday's result was the biggest ever electoral victory by an Italian centre-left party and one of the most decisive for any party in Italy since the heyday of the old Christian Democratic party following World War Two.
Along with German Chancellor Angela Merkel, the 39-year-old Renzi was one of the few of the continent's major leaders to see off the challenge of Eurosceptic parties, which swept to victory elsewhere.
He immediately pressed for a change in the policies that have dominated the European Union's response to the eurozone debt crisis since it flared up in 2010, repeating his calls for a focus on jobs and growth in place of pure budget austerity.
"Italy is in a position to put a decisive mark on the process that is now opening in Europe," Renzi told a news conference on Monday. "I consider this a vote of extraordinary hope for a country that has all the conditions to be able to change and that can invite Europe to change."
The scale of the victory in a country struggling to emerge from a prolonged economic slump gives Renzi legitimacy to tackle an ambitious programme of reforms laid out earlier this year after he staged a dramatic political coup that gave him control of an unwieldy coalition government.
Some observers say Sunday's success would allow Renzi to call snap national elections and consolidate his power in parliament. But Renzi dismissed the idea, saying parliament should continue to its natural end in 2018.
Renzi will also have a stronger hand in Europe. Italy's Democratic Party will become the second-largest group in the Strasbourg-based legislature after Merkel's centre-right bloc, and the biggest in the Party of European Socialists.
His victory also poses a challenge. With a strong mandate to reform, he now has few excuses for failing to deliver.
Shares in Italian banks rallied, and the FTSE MIB outperformed other European equities markets after Renzi's triumph over the Eurosceptic 5-Star. Italian bond yields fell.
Italy's premier repeated his pledge to respect commitments to EU partners to keep the country's public finances in check. He said he would not be seeking to change budget rules, rather the EU's overall "approach" to the economy.
With southern European economies on their knees and anger against mainstream parties rising across Europe, Renzi may find it easier to persuade Merkel to listen to his calls for greater focus on policies that encourage growth and jobs.
Italy's rotating six-month presidency of the EU, which begins in July, gives him a good platform to promote his agenda.
The fast-talking and telegenic Renzi, the former mayor of Florence, took power three months ago by forcing out his low-key predecessor Enrico Letta in a party coup.
In the run-up to the European election, Renzi cut income taxes for 10 million low earners and eased hiring rules for temporary workers in a bid to boost the economy, the euro zone's third-biggest, and lower high unemployment.
He has promised further tax cuts for businesses and households while cutting the country's 2-trillion-euro debt, and sweeping reforms of Italy's institutions, including a new electoral law and the abolition of the Senate to streamline Italy's often cumbersome lawmaking process.
Renzi heads a right-left coalition stitched together after the deadlocked 2013 national election. The New Centre Right (NCD), Renzi's coalition partner, won 4.4 percent of the vote, enough to stand on its own in the European Parliament after breaking away from Forza Italia last year.
The 77-year-old Berlusconi is serving a tax fraud sentence - public service at an old people's home - which prevented him from campaigning, which politicians from his party said was the reason for his party's disappointing showing.
Renzi called on Berlusconi to renew his support for institutional reforms, and urged 5-Star lawmakers to consider backing them to avoid further alienating its electorate.
With unemployment at just under 13 percent and the economy struggling to emerge from recession, many had expected to see a strong rise in support for Grillo's 5-Star Movement.
For both the former comic, whose rowdy and unconventional movement won a stunning 25.5 percent of the vote in national elections last year, and Berlusconi, the man who dominated Italian politics for 20 years, the result was a humiliation.
Berlusconi, barred from public office and prevented from voting after his conviction, said on his Facebook page the result was "below my expectations" but said he would return as he had after past defeats.
Grillo, whose popular blog was flooded with comments mocking his confident predictions of victory, appeared to blame voters, saying Italy appeared to be "made up of generations of pensioners who perhaps don't want to change".
He also posted a video of himself popping an indigestion pill. (Editing by Alessandra Galloni, Mike Peacock and Will Waterman)