TOKYO, July 4 (Reuters) - The dollar was on the back foot on Thursday after U.S. economic data continued to point to slowing growth, offering limited relief to the yen, which remained pinned near a 38-year low that had the market on alert for government intervention.

The euro and sterling both consolidated off three-week highs against the greenback, as voters hit the polls in the UK later in the day and investors awaited a second round of voting in France on Sunday.

The dollar index, which measures the greenback against a basket of peer currencies, was close to flat at 105.32 after briefly weakening to its lowest since June 13 at 105.04 on Wednesday.

Softer-than-expected U.S. economic data on Wednesday, including a weak services report and ADP employment report, depicted a slowing economy, following an increase in initial applications for unemployment benefits last week.

"Slowly but surely, what we're starting to see is a bit of a turn in the U.S. economic data flow," said Rodrigo Catril, senior currency strategist at National Australia Bank (NAB).

Minutes of the Fed's June meeting acknowledged the U.S. economy appeared to be slowing and "price pressures were diminishing."

The string of weaker economic data had markets pricing in about a 68% chance of a U.S. rate cut in September versus 56% a week ago, according to the CME FedWatch tool.

The dollar's drop helped a battered yen edge 0.12% higher versus the greenback to 161.53.

Traders also appeared to be adjusting positions ahead of Friday's closely watched U.S. nonfarm payrolls report, said Marita Ueda, general manager of the market research department at SBI Liquidity Market.

"Since Wednesday's (U.S.) employment-related indicators worsened, I think traders are becoming a little nervous that tomorrow's jobs data will also come in softer than expected."

Nonfarm payrolls are expected to show an increase of 190,000 jobs in June after a rise of 272,000 in May, according to a Reuters poll of economists.

But the Japanese currency was still stuck not far from a trough of 161.96 per dollar hit in the previous session, its lowest since December 1986, with fundamentals stacked against the yen.

Traders were preparing for possible Japanese government currency intervention with U.S. markets off for the July Fourth holiday. Tokyo's previous two rounds of yen buying occurred during illiquid points in the global trading day or holiday thinned trading.

The hurdle for intervening may be higher at this stage, said SBI Liquidity Market's Ueda.

"The Ministry of Finance is saying the trigger for intervention is not the level but if there are excessive moves. It's hard to step in since current moves don't fall into that category."

POLITICS IN THE SPOTLIGHT

Ahead of the U.S. jobs report, traders looked ahead to elections in the UK later on Thursday.

Britain looks set to elect Labour Party leader Keir Starmer as its next prime minister when voters go to the polls, sweeping Rishi Sunak's Conservatives out of office after 14 often turbulent years.

"There's a sense that a government with a majority and a new mandate that is likely to tack itself a little closer to Europe may provide a more fertile environment for the economy, and that should be positive for sterling," said NAB's Catril.

Sterling was holding steady after gaining on the dollar overnight, trading at $1.2739.

Analysts also pointed to more uncertainty concerning the French elections, with a run-off taking place on Sunday.

The euro was 0.02% lower at $1.0784, off its highest since June 12 against the greenback touched on Wednesday.

In cryptocurrencies, bitcoin slid 1.2% to $58,820.78, after slipping to a two-month low of $57,843 earlier in trading.

Ether stumbled to $3,172.60, its lowest since May 20, and was last down 0.8% at $3,228.88.

(Reporting by Brigid Riley; Editing by Jamie Freed)