* Stocks slide as coronavirus threat remains intense

* Dollar braces for U.S. manufacturing data

* Oil market slammed again by supply glut and weak demand

* Industrial metals hammered, bonds up on safety demand

* Hungarian forint at record lows by democracy worries

By Marc Jones

LONDON, April 1 (Reuters) - World markets fell on Wednesday as the coronavirus threat ensured an ugly start to April and the second quarter for equities and commodities.

Traders headed for the safety of government bonds, the dollar and gold as evidence continued to mount that the virus was sending the global economy into a deep recession.

Tokyo's Nikkei slumped 4.5% after the worst plunge in factory activity in almost a decade. The pan-European STOXX 600 sank 2.7% and Wall Street futures dived 3% after a dire forecast of likely U.S. coronavirus deaths.

"President Trump warning about two dreadful weeks ahead and 100,000 - 240,000 deaths in the coming months is definitely putting a negative tone on the market," said Societe Generale strategist Kit Juckes. "It is pretty risk-off out there. It is definitely a day of lower bonds yields, falling equity indexes and tin hats."

Wall Street tumbled on Tuesday, capping the biggest quarterly fall since 1987 for the Dow Jones and the steepest for the S&P 500 since the financial crisis. The fact it all happened in a month and from record highs made it feel all the more brutal.

U.S. economic activity is likely to be "very bad" and the unemployment rate could rise above 10% because of efforts to slow the spread of the coronavirus, Cleveland Federal Reserve Bank President Loretta Mester told CNBC.

There had been some glimmers of hope during Asian trading. China's factory activity improved in March after plunging in February. It just scraped into positive territory, beating analysts' expectations.

Blue-chip Chinese stocks failed to hold their gains, however, though Australian shares did bounce a tidy 3.5% as a slowdown in new coronavirus cases there and rising iron ore prices lifted the market.

But Europe's morning plunge meant MSCI's main gauge of world stocks was down nearly 1% having slumped 22% since the start of the year.

The number of coronavirus infections globally headed toward 800,000. In a positive development, Deutsche Bank analysts noted the global growth in new cases was below 10% for two consecutive days, having exceeded that rate for most of the past two weeks.

Health officials were not upbeat, however. A World Health Organization official warned that even in the Asia-Pacific region, the epidemic was "far from over." Deutsche had also warned the world's six main advanced economies would shrink between 4% and 9% this year.

APRIL FALLS

In currency markets, the dollar's safe-haven appeal saw it continue to rise. The yen held its ground, but the euro was back under $1.10 as key euro zone manufacturing data sank to lowest since mid-2012, when the currency union's debt crisis was raging.

The pound fell to $1.2350 and plenty of commodity-exposed currencies from the Australian dollar to the Russian rouble saw as much 1% losses.

Markets in Eastern Europe were hit too, with Poland's zloty down over 1% after grim data there and Hungary's forint tanking 2.5% as worries remained about open-ended powers granted to Prime Minister Viktor Orban to fight the coronavirus.

"In my view, markets have still not fully priced in the damage from the coronavirus, with some people still talking about V-shaped recovery," said Masahiko Loo, portfolio manager at Alliance Bernstein in Tokyo.

"The U.S. and Europe are hit by the first wave now, but as you can see in Asia, there could be more waves from re-imported cases. Human psychology also does not quickly recover either after an experience like this."

Demand for the guaranteed income of government bonds pushed the yield on the benchmark 10-year U.S. Treasury note down to 0.63%.

Italian bond yields also held steady as the benefit of recent European Central Bank measures meant the country - which has been one of those hit hardest by the coronavirus - successfully sold 8.5 billion euros of debt.

Commodity markets were much rougher. Brent crude fell nearly 6% at one point to as low as $24.80 per barrel as the United States, Russia, and Saudi Arabia jostled over a massive oversupply of oil.

Crude oil benchmarks ended the first quarter with their biggest losses in history. Both U.S. and Brent futures got hammered throughout March by the pandemic and a Saudi-Russia price war.

Global demand has been cut sharply by travel restrictions. Forecasters at major merchants and banks see demand slumping by 20% to 30% in April, and for weak consumption to linger for months.

(Reporting by Marc Jones; Editing by Toby Chopra)