* Conte promises better relations with Europe
* Urges new coalition partners to avoid arguments
* Government wins confidence vote in lower house
* Far-right stages protest in front of parliament (Adds govt winning confidence vote in lower chamber)
By Giuseppe Fonte and Crispian Balmer
ROME, Sept 9 (Reuters) - Italy's prime minister said on Monday his new coalition combining the anti-establishment 5-Star Movement and the pro-Europe Democratic Party (PD) would usher in a wave of reforms and avoid the rows that stymied his old government.
In a speech to parliament unveiling his policy priorities, Giuseppe Conte called for smoother relations with the European Union, saying he would work with Brussels to rewrite the bloc's budget rules and its immigration laws.
The PD and 5-Star agreed to join forces under Conte's leadership after the far-right League walked out of the previous, argumentative coalition with 5-Star in a failed effort to trigger early elections.
"We want to put behind us the din of useless declarations and belligerent, bombastic statements," Conte, a law professor with no political affiliation, told an often rowdy lower house before winning a vote of confidence in his administration.
"The language of this government will be mild-mannered," he added, in a swipe at the League's outspoken leader, Matteo Salvini.
His 90-minute speech was regularly interrupted by chants of "Elections! Elections!" from League politicians, while outside the lower house, hundreds of far-right supporters staged a noisy demonstration to demand a snap poll.
"They can run away from the vote for a few months, but they can't run away for ever, and when Italians get to vote we will win," Salvini told the cheering crowd. Some of those present gave stiff-armed fascist salutes.
Conte laid out a wide-ranging policy programme, promising expansionary measures to boost the stagnant economy, pledging to head off a big VAT increase set to kick in on Jan. 1 and warning that tax cheats in future would face prison terms.
He also said his government, Italy's 67th since World War Two, would forge ahead with legislation to cut the number of parliamentarians and introduce a new electoral law -- a fourth stab at rewriting voting rules since 2005.
The prime minister won the obligatory vote of confidence by 343 to 263 in the 630-seat lower house. He will face another such motion in the upper house Senate on Tuesday, where his coalition will have to govern with a much smaller majority.
"It is going to be difficult and complicated. A sense of responsibility has prevailed. Now we must roll up our sleeves and try to do the best for the country," said Culture Minister Dario Francheschini, a senior PD representative.
Conte's first government took office in June 2018, but soon got bogged down in rows over everything from infrastructure projects to immigration, and from EU relations to autonomy for Italy's wealthy north.
Salvini boosted his popularity with an uncompromising crackdown on boat migrants from north Africa, refusing to let charity rescue ships from docking in Italy.
Conte said he hoped to devise a new policy with Brussels of sharing migrant arrivals around the 28-nation bloc. He also promised a more constructive partnership in trying to revise EU banking norms and loosening budget restraints.
Looking to reset Italy's rocky EU ties, Conte has entrusted the mainstream PD with the EU affairs ministry and the economy ministry and has also dispatched former PD prime minister Paolo Gentiloni to Brussels as an EU commissioner.
Freed from the shackles of any ties to the eurosceptic League, Conte will fly to Brussels on Wednesday for the first foreign visit of his new premiership. He mentioned the word "Europe" and "European" some 32 times in his 27-page speech.
"I remain firmly convinced ... that it is within the confines of the European Union and not outside, that we must work for the good of Italians," he said.
Reporting by Angelo Amante, Giuseppe Fonte, Valentina Za and Silvia Aloisi; Writing by Crispian Balmer, Editing by Timothy Heritage