(Recasts lead, adds European futures, updates levels throughout)

* Asian stock markets : https://tmsnrt.rs/2zpUAr4

* Asian shares in the red, Japan closed for holiday

* Lofty share valuations, fading U.S. stimulus major risks

* Fresh wave of coronavirus infections in Europe also a worry

* Currencies steady, U.S. dollar near 3-1/2 mth low on yen

By Swati Pandey

SYDNEY, Sept 21 (Reuters) - Asian shares slipped on Monday on fears the global economy may sputter for a while due to a resurgence of coronavirus infections in Europe, while fading hopes for U.S. fiscal stimulus hopes also weighed.

The gloom spread to early European trade with pan-region Euro Stoxx 50 futures and German DAX futures both down 0.9%, while France's CAC 40 futures stumbled 0.6%. Futures for London's FTSE were off 1.1%.

S&P 500 e-minis declined 0.6%, also pointing to a weak start for Wall Street on Monday.

Most major Asian indexes were in the red and MSCI's broadest index of Asia-Pacific shares outside Japan was 0.6% weaker at 565.75.

Australia's benchmark index slipped 0.7% while New Zealand's faltered 0.8%. Chinese shares were lower too with the blue-chip index down 0.8%. Japanese markets were closed for a public holiday.

"While the economic recovery continues, momentum is clearly slowing," Kathy Bostjancic, chief U.S. financial economist at Oxford Economics, wrote in a note.

"The second phase of the recovery will likely be bumpy and fraught with pitfalls," Bostjancic added.

"The development of the pandemic remains the overriding factor driving the economy, discussions on the fiscal policy, and ultra loose policy by the Fed."

The biggest threat to world growth is a resurgent pandemic - coronavirus cases have now surpassed 30 million globally - with analysts fearing growth and inflation could surprise on the downside in the coming year. A lack of material development on U.S. stimulus package is also an overhang, they said.

Adding to worries, European countries from Denmark to Greece announced new restrictions on Friday to curb surging coronavirus infections in some of their largest cities, while Britain was considering a new national lockdown.

"Where is the inspiration for the equity bulls, I ask? We have diminishing prospects of fiscal stimulus, crazy valuations and a firm focus on an ugly U.S. election and COVID shutdowns, which suggest short-term risks for equities," said Pepperstone strategist Chris Weston.

The dollar slipped 0.1% against a basket of major currencies to 92.848.

Against the safe haven yen, the greenback eased 0.2% to 104.33 to drift closer to a recent 3-1/2 month trough.