TOKYO (Reuters) -The dollar was firm on Monday as the euro hovered near a more than one-month low amid political turmoil in Europe, while investors awaited fresh clues on the strength of the U.S. economy.

Investors have been contemplating the risk of a budget crisis at the heart of the euro area, as far right and leftist parties gain momentum ahead of France's surprise parliamentary election, pressuring President Emmanuel Macron's centrist administration.

Even after the French financial markets endured a brutal sell-off late last week, European Central Bank policymakers have no plans to discuss emergency purchases of French bonds, five sources told Reuters.

The euro inched down 0.04% to $1.07025, after falling to its lowest since May 1 at $1.06678 on Friday. The currency also logged its biggest weekly decline since April at 0.88% last week.

Although the political turmoil is a euro-bearish story, "as the euro accounts for around 57% of the US dollar index weighting, the fall of the euro has indirectly benefited the dollar," said Matt Simpson, senior market analyst at City Index.

The dollar index, which measures the greenback against a basket of peer currencies, was unchanged at 105.54, after touching its highest since May 2 at 105.80 on Friday.

Minneapolis Federal Reserve President Neel Kashkari said on Sunday it was a "reasonable prediction" that the U.S. central bank would cut interest rates once this year, waiting until December to do it.

The Fed published updated projections last week that showed the median forecast from all 19 U.S. central bankers was for a single interest rate cut this year.

This week is light on major U.S. economic data to help clarify the Fed's outlook, although U.S. retail sales on Tuesday and flash PMIs on Friday may give hints about consumption and economic strength.

"Data would likely have to miss estimates by a wide margin to rekindle bets of more Fed cuts, with the FOMC meeting still freshly in the minds of investors," said City Index's Simpson.

Sterling held steady at $1.2681. Britain's inflation pressures still appear too hot for the Bank of England to cut rates at its June 20 meeting, with a majority of economists polled by Reuters forecasting the first cut would not come until Aug. 1.

Elsewhere, the yuan was flat at 7.2557 per dollar after domestic data showed a mixed economic picture in China.

The offshore Chinese yuan held around 7.2694.

New home prices fell at the fastest pace in more than 9-1/2 years in May as the property sector struggles to find a bottom, while May industrial output came in below forecasts.

Retail sales were better than expected.

China's central bank left a key policy rate unchanged as expected on Monday as the weak yuan continued to hamper policy easing.

The yen remained pinned near a 34-year low against the dollar after the Bank of Japan on Friday pushed cuts to bond buying amounts and details of its tapering plan to its July policy meeting.

Governor Kazuo Ueda said he would not rule out raising interest rates in July as weakness in the yen pushes up import costs, although that may not be the hawkish statement that some took it to be, said Hiroyuki Machida, director of Japan FX and commodities sales at Australia & New Zealand Banking Group.

"The sense was that raising rates and tapering are two separate things" that the BOJ will decide whether or not to do based on different criteria, he said.

The yen steadied at 157.45, after slipping to 158.26 after Friday's decision, its lowest since April 29.

The yen's decline to 160.245 per dollar at the end of April triggered several rounds of official Japanese intervention totaling 9.79 trillion yen.

In cryptocurrencies, bitcoin last rose 1.1% to $66,454.38.