PARIS (Reuters) -French President Emmanuel Macron's centrist alliance would lower power bills, soften inheritance tax and link pensions to inflation if it wins a snap election, the prime minister said, seeking to counter the far right and a new left-wing bloc.

The ruling Together alliance is the underdog in the parliamentary vote, which Macron called after suffering a drubbing at the hands of the far-right National Rally (RN) in this month's European elections.

The snap legislative election will take place in two rounds on June 30 and July 7. Macron's camp casts itself as a bulwark of democratic values and prudent economic management protecting the nation from profligate extremists on both flanks.

Prime Minister Gabriel Attal said the policies advocated by both the RN and a rebranded coalition of left-wing parties known as the Popular Front would lead to mass unemployment.

"Let's not take a leap into the unknown, from a great height without a parachute," he said at a news conference.

The RN and the Popular Front, setting out their own stalls at an event run by the Medef, an employers' organisation, both presented themselves as responsible economic managers, seeking to rebut the attacks from the Macron camp.

"I think that overall our budget deficit won't be worse than what the current government foresees," said Eric Coquerel of the hard-left France Unbowed party, appearing on behalf of the Popular Front.

RETIREMENT AGE

Coquerel said the extra spending promised by the bloc on measures such as lowering the retirement age would be funded by stronger economic growth and higher tax revenues from the wealthy.

RN president Jordan Bardella, who would likely be prime minister if the far-right party wins a majority in the election, told the Medef he would introduce a revised 2024 budget over the summer, and measures would include cutting production taxes on companies.

Seeking to strike a reassuring tone after the prospect of his party winning power unnerved financial markets, Bardella said the state of France's public finances meant the next government would have to be realistic and responsible.

"I've understood that I need to reassure people," he said. "I want to return to budget sanity."

Battling for the centre, Attal said the ruling party's number one priority was to help households with their purchasing power, through measures such as lower electricity bills, linking pensions to inflation and help for first-time property buyers.

"There will be no tax hikes, no matter what," he said.

Turning to foreign policy, Attal said the far-right would threaten France's place in the European Union and its support for Ukraine, bringing the risk of "submission to Russia", and portrayed the left as fractious and disorderly, predicting diplomatic "cacophony" if it won.

"Europe and the world are watching us," he said.

(Additional reporting by Dominique Vidalon and Benoit Van Overstraeten; Writing by Estelle Shirbon; Editing by Richard Lough and Janet Lawrence)

By Elizabeth Pineau and Leigh Thomas