NEW YORK (Reuters) -Wall Street indexes fell on Thursday in choppy trade as a slump in Tesla shares offset news of progress in tariff talks between U.S. President Donald Trump and Chinese leader Xi Jinping.

Electric car-maker Tesla slumped over 9% in heavy trading as the public feud between CEO Elon Musk and Trump intensified. The stock has fallen four out of the last five sessions.

Musk has stepped up criticism of the president's massive tax legislation in recent days, while Trump alleged Musk was upset because the bill takes away tax benefits for electric vehicle purchases.

"The fallout for Tesla stock is self-evident," said Mark Spiegel, portfolio manager at Stanphyl Capital.

"I see no meaningful fallout from this for the rest of the market, other than its slight effect on the indexes and index funds. The overall stock market has plenty of problems, but Tesla isn't one of them."

Investors focused earlier on news that Trump and the Chinese leader had invited each other to their respective countries for future visits, U.S. and Chinese summaries of their phone call on Thursday showed.

A recent dispute over critical minerals threatens to tear up a fragile trade truce between the two biggest economies.

"Market stability will hinge on a trade agreement and not just a diplomatic exchange. Until we get a clear idea of what has been agreed or commitments made, this should be received with cautious optimism," said Julien Lafargue, chief market strategist at Barclays Private Bank.

At 2:10 p.m. the Dow Jones Industrial Average fell 16.83 points, or 0.04%, to 42,410.91. The S&P 500 lost 12.65 points, or 0.21%, at 5,958.16 and the Nasdaq Composite dropped 52.02 points, or 0.27%, to 19,408.47.

Weaker-than-expected U.S. private payrolls and services sector data on Wednesday raised concerns about an economic slowdown caused by trade uncertainties, with investors focusing squarely on Friday's nonfarm payrolls report.

Initial jobless claims data on Thursday showed Americans filing new applications for unemployment benefits last week rose for a second straight week.

The Federal Reserve is widely expected to hold interest rates steady at its next policy setting meeting this month.

Despite continued calls from Trump to slash rates, Fed Chair Jerome Powell has opted to stand pat so far, awaiting further data to guide the policy decision as tariff volatility prevails.

U.S. equities rallied sharply in May, with the S&P 500 index and the tech-heavy Nasdaq scoring their biggest monthly percentage gains since November 2023, thanks to a softening of Trump's harsh trade stance and upbeat earnings reports.

Brown-Forman fell nearly 17%, the most on the S&P 500, after the Jack Daniel's maker forecast a decline in annual revenue and profit.

Procter & Gamble said it will cut 7,000 jobs, or about 6% of its workforce, over the next two years, as part of a restructuring. Shares of the consumer goods bellwether fell 1.9%.

Advancing issues outnumbered decliners by a 1.47-to-1 ratio on the NYSE. There were 220 new highs and 42 new lows on the NYSE.

On the Nasdaq, advancing issues outnumbered decliners by a 1.02-to-1 ratio.

The S&P 500 posted 16 new 52-week highs and three new lows while the Nasdaq Composite recorded 50 new highs and 30 new lows.

(Reporting by Kanchana Chakravarty and Sukriti Gupta in Bengaluru and Saeed Azhar in New York; additional reporting by Carolina Mandl; Editing by Maju Samuel and Richard Chang)

By Saeed Azhar, Kanchana Chakravarty and Sukriti Gupta