*

Rightist bloc set for clear majority in both houses

*

Meloni would be country's first woman prime minister

*

League leader says government will be stable

*

Government not expected to be sworn in for few weeks

*

Record low turnout casts shadow over result

(Adds Meloni Facebook post in paragaphs 7-8)

By Keith Weir and Elisa Anzolin

ROME, Sept 26 (Reuters) - The right-wing alliance that won Italy's national election will usher in a rare era of political stability to tackle an array of problems besieging the euro zone's third largest economy, one of its senior figures said on Monday.

Giorgia Meloni looks set to become Italy's first woman prime minister at the head of its most right-wing government since World War Two after leading the conservative alliance to a triumph in Sunday's election.

Matteo Salvini, leader of the League party that is one of the main allies of Meloni's Brothers of Italy, shrugged off a poor showing by his own party and forecast an end to Italy's revolving-door governments.

"I expect that for at least five years we will press ahead without any changes, without any twists, prioritising the things we need to do," Salvini told a news conference.

Near final results showed the rightist bloc, which also includes Silvio Berlusconi's Forza Italia, should have a solid majority in both houses of parliament, potentially ending years of upheaval and fragile coalitions.

The result is the latest success for the right in Europe after a breakthrough for the anti-immigration Sweden Democrats in an election this month and advances made by the National Rally in France in June.

"Italians have given us an important responsibility," Meloni said in a social media post on Monday.

"It will now be our task not to disappoint them and do our utmost to restore dignity and pride to the nation," she said, alongside a picture of her clutching the country's flag.

Meloni, who has spoken out against what she calls "the LGBT lobby" and mass immigration, tries to play down her party's post-fascist roots and portrays it as a mainstream group like Britain's Conservatives.

She has pledged to back Western policy on Ukraine and not take risks with Italy's fragile finances.

TOUGH INHERITANCE

Meloni and her allies face a daunting list of challenges, including soaring energy prices, war in Ukraine and a renewed economic slowdown.

Her coalition government, Italy's 68th since 1946, is unlikely to be installed before the end of October and Prime Minister Mario Draghi remains at the head of a caretaker administration for now.