NEW YORK, July 27 (Reuters) - A sell-off in Chinese shares overnight in Asia extended the rout in U.S. markets on Tuesday, with a gap in volatility indexes signaling further weakness ahead, as tighter government regulations in China led investors to dump holdings. The iShares China Large-Cap ETF (FXI.P), which tracks an index of large Chinese companies that trade on the Hong Kong Stock Exchange, slid 3.3% and the Invesco Golden Dragon China ETF(PGJ.O), which mimics a Nasdaq index of the same name, fell 5.4%. The two ETFs closed at lows last seen in June 2020. Among well-known Chinese multinationals, e-commerce oriented Alibaba Group Holdings Ltd fell 3.0% and internet services company Baidu Inc lost 2.8%. The dive could get deeper as the gap between the Cboe China ETF Volatility Index(.VXFXI) and the Cboe Volatility Index (.VIX) - the so-called Wall Street "fear gauge" - grew to a record high 30 points. Past instances when the two volatility gauges have diverged widely have heralded further weakness for Chinese stocks, according to Chris Murphy, co-head of derivative strategy at Susquehanna International Group. What started off as a sell-off in equities bled into fixed income and foreign exchange markets earlier in Asia, sending the yuan falling through psychologically significant levels and pushing Chinese 10-year government bond futures down 0.35%, as traders scrambled to come to terms with the rout. The rout came after a shakeout on Monday spurred by new rules reining in China"s $120 billion private tutoring sector, sending some shares plunging more than 45%, and new regulatory moves targeting technology and property. read more Adding to broader concerns about the economic outlook, profit growth at China"s industrial firms slowed for a fourth straight month in June, as high raw material prices weighed on factories" margins. read more Reporting by Herbert Lash; Editing by David Gregorio Our Standards: The Thomson Reuters Trust Principles.