* Early signs of virus peaking in Europe, New York
* Broad gains from Tokyo to Sydney but momentum ebbs
* Currencies, bonds steady as economic risks weighed
* Asian stock markets: https://tmsnrt.rs/2zpUAr4
By Tom Westbrook and Chris Prentice
SINGAPORE/WASHINGTON, April 7 (Reuters) - Asian stock markets rallied for a second day on Tuesday, and riskier currencies rose, buoyed by tentative signs the coronavirus crisis may be levelling off in New York and receding in Europe.
Gains lacked Monday's momentum, but were broad, even though global coronavirus cases kept rising and an economic crash on a scale not seen for generations looms large.
The United States is bracing for its toughest week yet as the death toll climbs above 10,000 while across the Atlantic, British Prime Minister Boris Johnson has entered intensive care after his COVID-19 symptoms worsened. Nikkei .N225 rose 2% and has erased most of last week's losses after Prime Minister Shinzo Abe promised a massive $991 billion economic stimulus package - equal to 20% of GDP.
MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS pared early gains, but rose almost 1%. U.S. stock futures ESc1 eased 0.2% following a 7% surge on Wall Street on Monday. .N
Oil steadied and the risk-sensitive Australian dollar AUD=D3 rose 0.5%. FRX/
"The market is front running what it believes is a peak in the virus case count with Europe leading the way," said Chris Weston, head of research at Melbourne brokerage Pepperstone.
"You can almost smell the fear of missing out from active managers."
Worldwide there are 1.3 million cases and 70,395 deaths from COVID-19, the respiratory illness caused by the coronavirus - rising even as swathes of the globe are under lockdown. stems though from hardest-hit Italy and Spain, where authorities have started looking ahead to easing lockdowns after steady falls in coronavirus-related fatality rates.
In New York, the number of deaths each day has also steadied while hospitalisations, admissions to intensive care and the number of patients put on ventilators all declined.
Markets in Seoul .KS11 , Shanghai .SSEC and Hong Kong .HSI opened higher, then pared gains. Australia's ASX 200 .AXJO slipped into the red.
'PEAK DEATH WEEK'
Moves in the currency and bond markets were more muted, weighed by worries that lifting lockdowns too soon could drive a fresh wave of infections and caution about the economic fallout.
The U.S. dollar, which has soaked up safety flows for weeks, slipped on most majors. The Australian dollar AUD=D3 hit $0.6122, its highest in a week, but traders lacked confidence. AUD/
"It's a long way short of a serious rally," said Sean Callow, an FX analyst at Westpac in Sydney. "There is still so much bad news to absorb from the economy."
The New Zealand NZD=D3 rose 0.6% to $0.5958, while the safe-haven yen firmed 0.4% to 108.75 per dollar.
The United States has reported skyrocketing unemployment as lockdowns drive layoffs and is bracing for what one official called the "peak death week". twice as many people a day are now dying in the United States as in Spain or Italy, and hospitals report chaotic shortages of beds, ventilators and protective gear.
Benchmark 10-year U.S. Treasuries US10YT=RR nursed overnight losses, with yields steady at 0.6887%, having fallen almost 9 basis points on Monday. US/
Oil steadied amid hopes that the world's biggest producers of crude will agree to curtail production at a meeting to be held by video conference at 1400 GMT. O/R
Brent crude LCOc1 was up by 66 cents, or 2%, at $33.71 a barrel after falling more than 3% on Monday. U.S. crude CLc1 was up by 83 cents at $26.91 per barrel. Gold XAU= edged 0.2% lower to $1,657.31 per ounce.