U.S. President Joe Biden said on Tuesday he would be taking steps to fight the Omicron variant, by opening federal testing sites in New York City and buying 500 million at-home tests Americans can order online for free. Israel is set to offer a fourth dose of the COVID-19 vaccination to people over 60 years old.

World shares had fallen earlier in the week after Omicron infections multiplied around the world, but strong corporate earnings and reports that Moderna Inc's COVID-19 vaccine provides protection against the variant gave investors hope on Tuesday. U.S. stocks had also taken a hit after Biden's $1.75 trillion spending bill was dealt a potentially fatal blow on Sunday.

"We think this was kind of overdue over the past couple of weeks. We're kind of set up for a rally in time for Santa Claus, which officially begins next Monday," said Scott Brown, technical market strategist at LPL Financial, explaining that a so-called Santa Claus rally can happen in the last five trading days of the year and first two of the new year.

"We think we've had a little bit of a washout. We saw a lot of fear rush into the market."

The Dow Jones Industrial Average rose 1.6% to 35,492.7, and the S&P 500 gained 1.78% to 4,649.23. The Nasdaq Composite added 2.4% to close at 15,341.09.

MSCI's gauge of stocks across the globe gained 1.61%.

Oil prices settled up more than 3% despite signs of improving supply and concerns the spread of Omicron would curb travel and crimp demand for fuel. [O/R]

Brent crude settled up $2.46, or 3.4%, at $73.98 a barrel, and U.S. West Texas Intermediate (WTI) crude rose $2.51, or 3.7%, to $71.12 a barrel.

The United States is considering cutting quarantine time for people with COVID-19. The CEO of Delta Air Lines asked the U.S. Centers for Disease Control and Prevention to slash quarantine time to five days from 10.

A somber U.S. trading session on Monday underscored market fears that rapidly rising cases of the coronavirus variant would yet again force governments around the world to impose lockdown measures, potentially choking off fragile economic recoveries from similar measures earlier in the year.

Still, investors on Tuesday were cautiously optimistic that the economic hit would be less severe this time, as they bought stocks and sold perceived safe-haven currencies such as the dollar and Japanese yen.

The U.S. Dollar Currency Index fell slightly as investors ploughed money into riskier currencies.

The yen, considered a safe-haven asset, was flat versus the greenback at 114.08 per dollar.

U.S. Treasury yields rose on Tuesday as traders set their sights on optimistic economic conditions, and brushed aside inflation fears at a 20-year bond auction.

Elsewhere, cryptocurrencies - which often offer a reliable gauge to risk sentiment - gained ground. Bitcoin added more than 4% after trending lower in recent weeks.

(Reporting by Jessica DiNapoli in New York; Additional reporting by Tom Wilson in London and Julie Zhu in Hong Kong; Editing by Paul Simao and Matthew Lewis)

By Jessica DiNapoli