By Ankur Banerjee

SINGAPORE (Reuters) - The euro fell on Monday as the French President Emmanuel Macron called a shock election after being trounced in the European Union vote by the far-right, while the dollar was steady ahead of the Federal Reserve meeting later in the week.

The euro fell to $1.0764, its lowest since May 9, in early trading in Asia. It was last down 0.24% at $1.0776 as investors weighed the implications of renewed political uncertainty in the euro zone's second-biggest economy in a key election year.

Eurosceptic nationalists made the biggest gains in European Parliament elections in the Sunday vote, an aggregated exit poll showed, prompting Macron to take a risky gamble to try to reestablish his authority.

"The prospects of a far right victory in France's snap elections may keep the euro under pressure in the near term," said Mansoor Mohi-Uddin, chief economist at Bank Of Singapore.

"But the exchange rate is still more likely to be influenced by this week's U.S. inflation data and FOMC meeting."

The European Central Bank cut rates last week in a well-telegraphed move, but offered few hints about the outlook for monetary policy given that inflation is still above target.

The dollar index, which measures the U.S. currency against six rivals, was at 105.09, the highest since May 30, after rising 0.8% on Friday following data that showed the world's largest economy created a lot more jobs than expected in May.

U.S. nonfarm payrolls expanded by 272,000 jobs last month, data showed, while economists polled by Reuters had forecast payrolls advancing by 185,000.

Ryan Brandham, head of global capital markets for North America at Validus Risk Management, said recently the U.S. labour market data has been showing some signs of softening, supporting discussions of rate cuts in the second half of 2024.

"But this result will likely take the steam out of that conversation. The Fed has shown patience in waiting for the confidence that inflation will fully return to target before signalling rate cuts, and that caution seems warranted."

The jobs data led traders to once again shift their expectations of when the Fed will cut rates and by how much. Markets are now pricing in 36 basis points of cuts this year compared to nearly 50 bps - or at least two cuts - before the jobs data.

The chances of a rate cut in September are now at roughly 50%, from around 70% late on Thursday.

The Fed is not expected to make any change at its policy meeting this week but the focus will be on the comments from Fed Chair Jerome Powell and changes to economic projections from the policymakers. U.S. inflation data is also due on Wednesday.

"We suspect that the median dot will fall from three cuts to less than two. A hawkish hold?," said Marc Chandler, chief market strategist at Bannockburn Global Forex in New York.

The Bank of Japan is due to hold its two-day monetary policy meeting this week, with the central bank widely expected to maintain short-term interest rates in a 0-0.1% range.

The policymakers are brainstorming ways to slow its bond buying and may offer fresh guidance as early as this week, sources familiar with its thinking told Reuters, in what would be a first step to reducing its almost $5 trillion balance sheet.

The Japanese yen weakened to 156.95 in early trading on Monday. The currency remains close to the 34-year trough beyond 160 per dollar reached at the end of April, which prompted Japanese officials to spend some 9.8 trillion yen ($62.46 billion) intervening in the currency market to support it.

Sterling was flat at $1.2723 having touched $1.2700, its lowest in a week earlier in the session.

($1 = 156.9000 yen)