* Asian stock markets : tmsnrt.rs/2zpUAr4 * China shares edge up, still down sharply on week * Fed sees progress on economy, but not there yet * Senate passes infrastructure bill, more votes ahead * Facebook stock down after warning on revenue growth SYDNEY, July 29 (Reuters) - Asian shares managed a modest bounce on Thursday as the U.S. Federal Reserve signalled it was in no rush to taper stimulus, though the mood was fragile as investors waited to see if Beijing could stem the recent rout in Chinese shares. There was also some promising news on the long-awaited U.S. infrastructure bill as the Senate voted to move ahead on the $1.2 trillion deal. China’s markets edged higher amid reports regulators had called banks overnight to ease concerns about tighter rules on the education sector and on overseas listings. “The message is that profit has not become a dirty word in the Chinese system of ‘Socialism with Chinese characteristics’, only in certain sectors,” said Ray Attrill, head of FX strategy at NAB. “How successful the messaging by the authorities will be in putting a floor under the broader Chinese stock market remains to be seen.” For now, gains were tentative with blue-chip shares up 1.6%, but still down 5% for the week so far, while the Shanghai Composite Index added 1.2%. MSCI’s broadest index of Asia-Pacific shares outside Japan bounced 1.9%, having slid to its lowest since early December on Wednesday. Japan’s Nikkei edged up 0.6%, while South Korea was flat. S&P 500 futures eased 0.1%, as did EUROSTOXX 50 futures. Nasdaq futures dipped 0.3% perhaps weighed by a retreat in Facebook stock. Facebook Inc shed 3.5% after the company warned revenue growth would “decelerate significantly,” even as it reported strong ad sales. Markets had see-sawed overnight when the Federal Reserve policy statement said “progress” had been made toward its economic goals, seeming to bring nearer the day when it might start tapering its massive asset buying campaign. Data due later Thursday is expected to show the U.S. economy likely grew at the fastest pace in 38 years last quarter as government aid and vaccinations fuelled spending. However, Fed Chair Jerome Powell took a dovish turn by emphasising that they were “some ways away” from substantial progress on jobs that is needed to start tapering. “The difference in tone between the statement and press conference may simply reflect Powell being on the dovish side of the Committee,” said JPMorgan economist Michael Feroli. “In any event, there are three more job reports before the November meeting, and two more between the November and December meetings,” he added. “We continue to expect a December announcement, though we see a risk it could occur in November.” The next Fed meeting is not until late September, offering the market a break from tapering talk. For bonds, the net result was that U.S. 10-year yields were steady at 1.24%, not far from recent five-month lows of 1.128%. The pattern was the same for the dollar, which edged up on the FOMC statement only to flag on Powell’s remarks. That left the euro up at $1.1855, and some way from its recent four-month trough of $1.1750. The dollar faded to 109.75 yen, from a top of 110.58 early in the week. All of which saw the dollar index dip to 92.157, off its recent top at 93.194. In commodity markets, gold nudged up to $1,815 an ounce but remains in the $30 range of the past 17 sessions. Oil prices firmed after data showed U.S. crude inventories fell to pre-pandemic levels, bringing the market’s focus back to tight supplies rather than rising COVID-19 infections. Brent was last up 26 cents at $75.00 a barrel, while U.S. crude added 28 cents to $72.67. Editing by Ana Nicolaci da Costa & Simon Cameron-Moore Our Standards: The Thomson Reuters Trust Principles.