Much of the concern over the global outlook has been driven by the Omicron variant of coronavirus.
Germany’s leaders were set to decide on new restrictions after Christmas aimed at slowing the spread of Omicron, but plans so far fall short of a full lockdown.
In Frankfurt, the DAX jumped 0.9% to 15,381.41 and the CAC 40 in Paris also gained 0.9%, to 6,928.88.
In Asia, cases of coronavirus have surged in Australia and South Korea, as governments tighten precautions to prevent or curb outbreaks.
Tokyo’s Nikkei 225 index rose 2.1% to 28,517.59 and the Hang Seng in Hong Kong added 1.2% to 23,024.78.
Worries that the newest coronanvirus variant could lead factories, airplanes and drivers to burn less fuel pulled oil prices lower, but they also rebounded Tuesday, with the U.S.
Markets are also still absorbing last week’s momentous move by the Federal Reserve to more quickly remove the aid it’s throwing at the economy, because of rising inflation.
Renewed virus outbreaks could push inflation even higher if they result in closures at ports, factories and other key points of the long global supply chains.