They started the week on a high but by Tuesday (Sep 29) European stock market rebounds had largely fizzled out.
Investors were cautious ahead of the first U.S. presidential debate, with the pan-European STOXX 600 slipping 0.5% in early deals.
Growth-sensitive sectors such as banks, automakers and travel & leisure were down between 1.0% and 1.4%
It comes as a Reuters tally showed the global death toll from COVID-19 crossed 1 million.
Among the big movers in morning trade was Air France KLM.
It fell 3.9% after HSBC downgraded its stock.
Investors are awaiting the first U.S. presidential debate.
They're weighing the potential impact on the U.S. economy of either the re-election of Donald Trump.
Or a victory for Democratic presidential nominee Joe Biden.
Many see a Biden victory increasing the chances of further fiscal stimulus to counter the economic damage from the pandemic.
Earlier, MSCI's broadest index of Asia-Pacific shares outside Japan was flat, shedding earlier gains.
And Hong Kong's Hang Seng index lost 0.9%.
Asian markets have been buoyed by positive signs around China's economic recovery.
But continuing havoc caused by the pandemic has raised concern about high valuations.
Elsewhere, sterling extended its overnight gains on optimism about a Brexit trade deal.
The European Union and Britain are kicking off a decisive week of talks.