TOKYO -- Global shares rose Tuesday, fueled by hopes the peak of the coronavirus pandemic surge may come soon.

France's CAC 40 rose nearly 4.0% to 4,518.21 in early trading, while Germany's DAX jumped 4.5% to 10,530.95. Britain's FTSE 100 added 2.6% to 5,728.94.

U.S. shares were set to drift higher with Dow futures gaining 2.9% to 23,140. S&P 500 futures rose 2.7% to 2,716.12.

In Asia, Japan's benchmark Nikkei 225 gained 2.0% to finish at 18,950.18 ahead of Prime Minister Shinzo Abe's announcement of a state of emergency in Tokyo and six other regions. Abe was due to also outline details of a 108 trillion yen ($1 trillion) package to support the world's third-largest economy, including cash handouts to needy families and help for small businesses.

India's Sensex jumped 8.1%, to 29,816.45 in what analysts characterized as a technical rally.

Investors have been anxiously watching for signs that the rate of new infections may be hitting its peak, which would give some clarity about how long the upcoming recession will last and how deep it will be. Without that, markets have been guessing about how long businesses will remain shut down, companies will lay off workers and flights remain cancelled due to measures meant to slow the speed of the outbreak.

China on Tuesday reported no new deaths from the coronarivus over the past 24 hours. It had 32 new cases, all from people who returned from overseas. The country that gave rise to the global pandemic has recorded 3,335 deaths and nearly 82,700 total cases. Numbers of daily new deaths have been hovering in the single digits for weeks, hitting just one on several occasions.

The number of new coronavirus cases was dropping in the European hotspots of Italy and Spain. The centre of the U.S. outbreak, New York, also reported its number of daily deaths has been effectively flat for two days. Even though the U.S. is still bracing for a surge of deaths due to COVID-19 and New York's governor said restrictions should stay in place to slow its spread, the encouraging signs were enough to launch the S&P 500 to its best day in nearly two weeks.

The latest news has given investors at least a temporary excuse to resume buying.

South Korea's Kospi gained 1.8% to 1,823.60. Hong Kong's Hang Seng added 2.1% to 24,253.29, while the Shanghai Composite jumped nearly 2.1% to 2,820.76. But Australia's S&P/ASX 200 lost 0.7% to 5,252.30.

The S&P 500 is still down more than 21% since its record set in February, but the losses have been slowing since Washington promised massive amounts of aid to prop up the economy.

"Since this is a public health crisis, the response has been extreme," Morgan Stanley strategists wrote in a report. "There are literally no governors on the amount of monetary or fiscal stimulus that will be used in this fight."

ENERGY: Expectations have risen that Saudi Arabia and Russia may cut back on some of their production. Demand for oil has plummeted due to the weakening economy, and any cutback in production would help prop up its price. A meeting between OPEC, Russia and other producers initially planned for Monday was reportedly pushed back to Thursday.

Benchmark U.S. crude added 89 cents to $26.97 per barrel. It fell $2.26, or 8%, to settle at $26.08 a barrel Monday after surging nearly $7 last week. It started the year above $60 per barrel. Brent crude, the international standard, rose 55 cents to $33.50 a barrel.

CURRENCIES: The dollar fell to 108.88 yen from 109.24 yen Monday. The euro rose to $1.0865 from $1.0792.