By Chibuike Oguh and Marc Jones

NEW YORK/LONDON (Reuters) -Global shares hit their third record high in three days on Thursday while the U.S. dollar sank to its lowest level in more than three years amid growing market concerns about the Federal Reserve's independence.

The U.S. dollar index was down nearly 0.43% on the session and more than 10% for the year. If the greenback's losses hold until the month ends, it will be the biggest fall in the first half of a year since the start of the era of free-floating currencies in the early 1970s.

Wall Street's main indexes finished higher, with the benchmark S&P 500 and Nasdaq nearing record highs. The Dow Jones Industrial Average rose 0.94% to 43,386.84, the S&P 500 rose 0.80% to 6,141.02 and the Nasdaq Composite rose 0.97% to 20,167.91.

European shares finished up 0.09%. MSCI's gauge of stocks across the globe rose 0.81% to 909.47, hitting a new record high for the third straight session.

A Wall Street Journal report said President Donald Trump - who has been urging the Fed to cut rates faster - was toying with the idea of selecting Chair Jerome Powell's replacement in the next few months ahead of the end of his term next May.

Powell had just wrapped up two days of testimony to U.S. Congress, where he said the central bank would be careful in considering further rate cuts as it expects Trump's tariffs would cause prices to rise this summer.

Such an appointment by Trump of a shadow Fed chair will likely shake investor confidence in the central bank's independence, which is helping to contribute to the dollar's weakness, said Wasif Latif, chief investment officer at Sarmaya Partners in New Jersey.

"The market recognizes that sooner rather than later, Powell will walk off the stage and the next appointment will likely be somebody that's a little bit softer or dovish or somewhat politically driven," Latif said. "And the market is saying the next chair will likely be more amenable to big cuts than Powell has been and so I think that's part of what's feeding into the dollar weakness and gold is also reflecting that."

The euro is now at its strongest level against the dollar since September 2021 and trade tariff talks are looming with Washington next week, ahead of a Trump-imposed global deadline of July 9. The single currency was up 0.33% at $1.1697. [/FRX]

The dollar weakened to a decade and half-year low against the Swiss franc at 0.80030. It was also down 0.57% to 144.415 against the Japanese yen.

The dollar index, which measures the U.S. currency against six peers, now sits at its lowest level since March 2022 following its slide this year.