London’s benchmark FTSE 100 share index, which measures the share prices of the 100 most valuable companies traded on the London stock exchange, was up 0.5% in the opening minutes.
Earlier, Japan’s main share index closed down by more than 2%.
Investors remain worried over the continuing slide in oil prices and slowing growth in China.
On January 20, global stock markets suffered hefty losses and London’s FTSE 100 lost 3.5%.
It has now entered a “bear market”, having fallen 20% from its record high in April 2015.
In the first few minutes of trade on January 21, the FTSE 100 was up 31.78 points at 5,705.36.
Oil prices remained weak on January 21, having hit their lowest levels since 2003 in the previous session.
A brief rally in crude prices quickly ran out of steam, and after climbing back above the $28-a-barrel mark, Brent crude fell back to $27.79.
US crude was trading at $28.23 a barrel, having fallen below $27 on January 20.
Crude oil prices have been falling since mid 2014, but oil-producing countries have maintained output despite the decline, contributing to the excess supplies on the market.
Earlier in the week, the International Energy Agency warned that oil markets could “drown in oversupply” in 2016.
In Asia, Japan’s Nikkei 225 share index closed down 2.4%, while China’s Shanghai Composite ended the day down 3.2%.
On January 20, US shares had also been hit, with the Dow Jones closing 1.6% lower after a volatile trading day.
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