By Danilo Masoni

MILAN, Dec 15 (Reuters) - World shares steadied on Tuesday and currencies moved in tight ranges as rising COVID-19 cases and social restrictions before the Christmas shopping season offset optimism over a vaccine-driven economic recovery next year.

The MSCI world equity index, which tracks shares in 49 countries, was flat by 1201 GMT after losses in Asia overnight.

European shares were little changed.

Investors were also watching talks between London and Brussels on a trade deal after months of inconclusive discussions. They were keeping an eye on a U.S. fiscal stimulus talks, too, and on the Federal Reserve's last policy meeting of the year, which ends on Wednesday.

The number of coronavirus deaths in the United States exceeded 300,000 on Monday as the hardest-hit nation started its first vaccine inoculations, while tighter COVID-19 restrictions were imposed on London.

Other countries across Europe were also set to impose new restrictions during the holiday season to rein the contagion. Germany adopted a stricter lockdown on Sunday.

"Much of Europe will have to weather tighter restrictions until at least early to mid-January. Q4 will be lost quarter for growth, but that should surprise no one," said AFS analyst Arne Petimezas in Amsterdam.

"Markets remain bifurcated, with the solid post-vaccine advances for equities, credit and commodities intact. Bond yields refuse to budge though, and in particularly euro zone government bond yields remain terribly depressed," he said.

Most Asian share markets retreated on Tuesday.

MSCI's index of Asia-Pacific shares outside Japan fell 0.4% to its lowest in more than a week after a string of record highs in recent weeks.

China's blue chips, however, ended 0.2% higher, helped by upbeat factory data, which rose for an eighth month in a row as an economic recovery gathered pace.

Positive news on vaccines, along with a market-friendly outcome of the U.S.
presidential election that has bolstered hopes of greater fiscal stimulus, has powered gains over the last few weeks, lifting world shares to record highs.

A $908 billion COVID-19 relief plan in the United States will be split into two packages in a bid to win approval, a source said on Monday.

Lawmakers hope to attach the aid to a government funding measure that needs to be done by Friday.

On Tuesday, the MSCI world equity index was just 1.1% below its record high and was up 11% so far this year.

"FRIENDLY BACKDROP"

Last week, the United States authorised the emergency use of its first COVID-19 vaccine, developed by Pfizer and BioNTech.
The vaccine has already been authorised in a handful of countries, including Britain and Canada.

The opening of a U.S. vaccine programme did not prevent Wall Street from finishing lower on Monday.

"The start of vaccine approvals and distribution heightens our confidence in strong global growth in 2021. Combined with supportive policy and a fresh decline in U.S. real yields, this remains a friendly backdrop for cyclical and risky assets," said Goldman Sachs strategists.

"With the vaccine announcements behind us, and a sizable market response, it makes more sense to look for areas that have under-reflected the coming recovery," they added.

E-Mini futures for the S&P 500 rose 0.6%, pointing to a rebound.

On Monday, the S&P 500 closed down 0.4%, the Nasdaq gained 0.5% and the Dow Jones reached a record high but fell back 0.6% for the day.

In foreign exchange markets, the pound rose but remained below Monday's peak on growing optimism about the chances of post-Brexit trade deal.

However, volatility gauges pointed to further turbulence ahead as a Dec. 31 deadline approached.

It was last 0.4% up at $1.3379 after reaching a two-and-a-half-year high earlier this month.

The dollar traded near two-and-a-half-year lows as demand for the safest assets waned and investors eyed developments in the U.S.

stimulus talks.

U.S. Treasury yields inched up to 0.8998% before the Fed's two-day policy meeting. Expectations are growing expectations the Fed will further ease monetary policy by expanding its bond-buying programme.

"For once, there is a bit of uncertainty on the outcome," said Giuseppe Sersale, strategist at Anthilia in Milan. "The pandemic's fury and some weakening in macro data are seen as good reasons to take action. Personally I don't believe (the Fed has) reasons to change the current stance."

The Bank of England and the Bank of Japan also close out their 2020 meetings this week.

On bond markets, concerns about rising COVID-19 cases in major economies put further pressure on yields.

Germany's benchmark 10-year bond yield dipped to -0.627% , nearing recent one-month lows of around -0.64%.

Italy's and tester parfümler Greece's 10-year yield both fell to record lows.

Gold prices advanced 1% to $1,844.4 per ounce.

Brent crude oil prices were up 0.1% to $50.3 a barrel. Gains were capped by Europe's tighter lockdowns and an OPEC forecast for a slower recovery in demand next year.

London copper prices crept up, underpinned by the strong manufacturing output data from China.

(Reporting by Danilo Masoni in Milan, additional reporting by Anshuman Daga in Singapore; editing by Ed Osmond, Larry King)