A global rally on financial markets faded as US shares shed gains despite hopes that the spread of coronavirus in some hotspots may be easing.
The Dow Jones and the S&P 500 dipped 0.1%, while the Nasdaq fell 0.3%, dropping back from earlier increases and a 7% surge on Monday.
In London, Paris and Frankfurt stocks had closed more than 2% higher, while earlier Asian markets also gained.
A drop in oil prices contributed to the afternoon slide.
However, Tuesday's declines were modest compared to the dramatic swings in recent weeks, reflecting signs of renewed investor optimism for many companies - including travel companies and retailers, which had seen shares plunge as governments impose lockdown measures.
In the US, department store Kohl's jumped 20%, while Royal Caribbean Cruises climbed more than 13%. In the UK, Easyjet rose more than 15%, while British Airways' owner IAG increased 7%.
The FTSE 250, considered to be more representative of the UK economy, finished more than 5% higher.
Investor sentiment was buoyed by news that the death toll in Spain, which has been badly affected by the coronavirus pandemic, had fallen for a fourth consecutive day, in a sign that the country may have passed its peak.
There was also a slowdown of new infections in Italy, which has also been ravaged by the virus. News that some countries, including Austria and Denmark, have made small steps to relax their lockdowns, also helped sentiment.
But New York, which had earlier seen signs its outbreak might be easing, reported a large jump in Covid-19 deaths.
"Investors are reacting to indications that lockdown measures in the UK, US and Europe are beginning to 'flatten the curve' of coronavirus infections and fatalities," said Russ Mould, investment director at AJ Bell.
However, he added: "The market's relief is only likely to last so long, and attention will soon turn to how countries intend to exit the current containment measures which have in effect hit the pause button on the global economy."
Despite gains on Monday and Tuesday, the FTSE 100 is still down by 25% compared to its highest level in January, before the pandemic led to lockdowns across Europe and the US.
Adding to the positive financial news were further measures to support economies, including a trillion-dollar package in Japan and central bank moves in China.
And with the ink barely dry on a $2 trillion rescue plan passed by Congress last month, Donald Trump said he favoured another massive spending programme, this time targeting infrastructure projects.
There are also reports that European Union leaders are close to a rescue package for countries worst hit by the pandemic.