TOKYO—Asian shares took a beating on Friday after a fresh salvo of hawkish remarks from Federal Reserve officials solidified expectations that U.S. interest rates could rise as soon as March, leaving markets braced for tighter monetary conditions. Fed Governor Lael Brainard became the latest and most senior U.S. central banker on Thursday to signal that rates will rise in March to combat inflation. Equity markets turned deeply red with investors seeking shelter in safer assets such as government debt. MSCI’s broadest index of Asia-Pacific shares outside Japan shed 0.8 percent in mid-morning trade, while Australia lost 1.2 percent and Japan’s Nikkei shed 1.9 percent by the midday break. South Korean shares dropped 1.5 percent after its central bank raised its benchmark rate 25 basis points to 1.25 percent on Friday, taking it back to where it was before the pandemic as it seeks to restrain consumer price rises. China’s blue-chip …