French prime minister Francois Bayrou. Photo: AP

French prime minister Francois Bayrou. Photo: AP

Shares are falling sharply in Europe and fell overnight in Asia after US president Donald Trump announced he was firing Federal Reserve Governor Lisa Cook.

Mr Trump said in a letter posted on Monday on his Truth Social platform that he was removing Ms Cook because of allegations that she committed mortgage fraud, but the move is being interpreted as a direct attack on the independence of the US central bank, which Mr Trump has repeatedly pushed to lower interest rates.