* Bitcoin jumps more than 10%, ether more than 16% * Fed’s Brainard says focus sharpening on central bank cryptos * Fight back comes after miners suspend China operations * Beijing crackdown on crypto has spooked markets * Broad Sunday selloff leaves sector struggling for breath (Updates prices, adds Brainard comments, changes dateline (previously LONDON/SINGAPORE) By Tom Wilson, Tom Westbrook and Stephen Culp NEW YORK, May 24 (Reuters) - Cryptocurrencies rebounded on Monday, reclaiming ground lost during a bout of weekend selling that was fuelled by further signs of a Chinese crackdown on the emerging sector. Bitcoin was last up 8.8% to $37,766, erasing losses of 7.5% from a day earlier but still down by more than 40% from last month’s record high. Second-largest cryptocurrency ether jumped more than 17% to as high as $2,459 after slumping more than 8% on Sunday to near a two-month low. Yet it too has fallen by almost half from a peak hit earlier this month. In the past week policymakers have stepped up their response to the popularity, and volatility, of cryptocurrencies. On Monday Federal Reserve Governor Lael Brainard told a virtual conference organized by CoinDesk that the growth in “private money,” digital payments and steps by other central banks were sharpening the focus on Central Bank Digital Currencies (CBDC.) While her comments did not cause much of price move, she did say that the wide use of private money poses consumer and stability risks given possible “run-like behavior.” The catalyst for the Sunday slump was cryptocurrency “miners” - who mint cryptocurrencies by using powerful computers to solve complex maths puzzles - halting Chinese operations in the face of increasing scrutiny from authorities. The attention on miners in China - who account for some 70% of supply - is the latest front in a wider push by Beijing against the cryptocurrency sector. Major cryptocurrency exchange Huobi on Monday suspended both crypto-mining and some trading services to new clients from mainland China, adding it would instead focus on overseas businesses. Others also suspended business in China. In the short-term, market players said, that is likely to lead to pressure on prices as miners sell bitcoin held on their balance sheets. “If they are pulling up stakes or shutting down, they may need to reduce their balance sheets in the short term,” said James Quinn, managing partner at Q9 Capital, a Hong Kong-based cryptocurrency private wealth manager. ‘TOUGH SPOT’ Crypto market players said fears over the China crackdown would likely linger. “Nobody’s really sure about what happens next,” said Joseph Edwards, head of research at crypto brokerage Enigma Securities. “Crypto clearly finds itself in a tough spot in terms of the narrative right now, and it’s taken a lot of oxygen out of the room.” Bitcoin had stabilised from a bruising week on Saturday after Tesla boss Elon Musk - whose comments on cryptocurrencies have been a key price driver in recent months - tweeted support for crypto in “the true battle” with fiat currencies. Yet after last week’s 25% drop, triggered in part by toughening language from Chinese regulators, bitcoin remains over 40% below last month’s record high of $64,895. “It is too early to call the end of the recent bitcoin downtrend,” J.P. Morgan analysts wrote. Publicly listed bitcoin funds saw outflows of more than $530 million last week, their fifth straight week of loses, they said, in a sign of retrenchment by institutional investors. (Reporting by Stephen Culp in New York, Tom Wilson in London and Tom Westbrook in Singapore; Editing by Sam Holmes, Robert Birsel, Andrew Heavens and Andrea Ricci) Our Standards: The Thomson Reuters Trust Principles.