Global equity indices mostly rose on Tuesday, with Wall Street rebounding from a weak start to the year, and oil prices settled up 5 per cent after news that Saudi Arabia will make voluntary cuts to its oil output in February.

Investors anxiously awaited the results of two Senate run-off races in the state of Georgia on Tuesday that are expected to determine the balance of power in Washington.

A Democratic victory in both contests could tip control of the US Senate away from Republicans, potentially boosting the agenda of Democratic President-elect Joe Biden.

"Investors are taking a wait-and-see attitude ... There's a lot to be concerned about - not only in the US with the elections, but also because of the different strains of the virus that are now being reported around the globe," CFRA chief investment strategist Sam Stovall said.

Georgia results are expected to be known by Wednesday morning, according to state officials. No Democrat has won a Senate race in Georgia in two decades, but opinion surveys show both races as exceedingly close.

The start of vaccine roll-outs boosted equities heading into the end of the year, and US stocks ended 2020 at record highs.

The discovery of a more contagious variant of the coronavirus and the latest virus-related restrictions have offset some of that optimism. Britain has begun its third national lockdown, and New York on Monday reported its first case of the coronavirus variant.

The Dow Jones Industrial Average rose 167.71 points, or 0.55 per cent, to close at 30,391.6, the S&P 500 gained 26.21 points, or 0.71 per cent, to 3,726.86 and the Nasdaq Composite added 120.51 points, or 0.95 per cent, to 12,818.96.

The pan-European STOXX 600 index lost 0.19 per cent and MSCI's gauge of stocks across the globe gained 0.62 per cent.

US crude futures climbed 4.9 per cent to settle at $49.93 a barrel. Brent crude futures also jumped 4.9 per cent, settling at $53.60.

Saudi Arabia pledged additional, voluntary oil output cuts of 1 million barrels per day (bpd) in February and March as part of a deal under which most producers from the Organization of the Petroleum Exporting Countries and allies will hold production steady in the face of new coronavirus lockdowns.

In the currency markets, the dollar fell against a basket of major currencies in the wake of China's decision to lift its official yuan exchange rate by its highest margin since it abandoned a dollar peg in 2005.

The Chinese move helped support demand for other currencies.

In the offshore market, the yuan strengthened as far as 6.4419 for the first time since June 2018. It started the week at 6.4944.

The British pound recovered from a tumble on Monday, when a surge in Covid-19 cases in the UK forced the nationwide lockdown until mid-February.

The dollar index fell 0.418 per cent, with the euro up 0.35 per cent to $1.2291. Sterling was last trading at $1.362, up 0.38 per cent on the day.

Bitcoin traded at $34,077.96, up 6.41 per cent, following a roller-coaster ride that took it to a record high of $34,800 on Sunday and a subsequent tumble to as low as $27,734 the following session.

Spot gold added 0.4 per cent to $1,949.46 an ounce.

In the bond market, benchmark US 10-year notes last fell 12/32 in price to yield 0.9549 per cent, from 0.917 per cent late on Monday.

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