European stock markets rebounded Tuesday from the sharp coronavirus-related falls seen a day earlier, while Wall Street equities were mixed following lackluster US data.

European markets had a good day despite grinding talks over Brexit and lingering unease over the latest coronavirus trends.

The EU has rejected the latest UK offer on fishing but is ready to pursue a post-Brexit trade deal even beyond the end of the year, diplomats said.

Meanwhile, the European Commission recommended that EU member states lift the blanket bans some have imposed on travel from Britain in response to a new strain of Covid-19.

The new variant of the virus, which also has been detected in small numbers elsewhere, appears to spread more easily than other types but experts say there is no evidence it is more lethal or resistant to vaccines.

After dropping around two percent or more, bourses in London, Paris and Frankfurt all advanced, with analysts pointing to positive sentiment after the US Congress approved a new $900 billion relief package after months of negotiations.

Back in the US, the Nasdaq closed at a fresh record but the Dow and S&P 500 finished lower amid more worrisome economic data.

"Worry over the impacts of the virus and the subsequent new restrictions are tamping down some of the early enthusiasm that came amid passage of a long-awaited fiscal relief and government spending package," Schwab analysts said.

Data showed consumer confidence falling for a second straight month, while existing home sales fell for the first time in six months, more signs of the drag from the rising coronavirus cases.

"Consumers' assessment of current conditions deteriorated sharply in December, as the resurgence of COVID-19 remains a drag on confidence," The Conference Board's Lynn Franco said in a statement on the consumer data.

David Kelly at JPMorgan Asset Management said the US stimulus bill "will help some workers and businesses get through the winter, but it will do little to accelerate the arrival of an economic recovery."

Among individual companies, Apple jumped 2.9 percent amid reports the tech company aims to launch its autonomous car in 2024.

Walmart dropped 1.2 percent after the US Justice Department sued the retail giant over its role in the opioid crisis, alleging the giant retailer wrongly filled prescriptions and worsened a public health disaster.

Walmart said the charges were baseless and an effort by authorities to shift blame away from their role in the debacle.

Alaska Air Group gained 0.3 percent as it sealed a deal to add 23 more Boeing 737 MAX planes to its order, saying the transaction would boost move it toward a single fleet that would be more efficient and cost-effective. Boeing dropped 0.2 percent.

The Dutch are preparing for a possible back up of lorries heading for Britain
The Dutch are preparing for a possible back up of lorries heading for Britain ANP / Marco de Swart

New York - Dow: DOWN 0.7 percent at 30,015.51 (close)

New York - S&P 500: DOWN 0.2 percent at 3,687.26 (close)

New York - Nasdaq: UP 0.5 percent at 12,807.92 (close)

London - FTSE 100: UP 0.6 percent at 6,453.16 (close)

Frankfurt - DAX 30: UP 1.3 percent at 13,418.11 (close)

Paris - CAC 40: UP 1.4 percent at 5,466.86 (close)

EURO STOXX 50: UP 1.4 percent at 3,497.49 (close)

Tokyo - Nikkei 225: DOWN 1.0 percent at 26,436.39 (close)

Hong Kong - Hang Seng: DOWN 0.7 percent at 26,119.25 (close)

Shanghai - Composite: DOWN 1.9 percent at 3,356.78 (close)

Pound/dollar: DOWN at $1.3375 from $1.3464 at 2200 GMT

Euro/pound: UP at 90.94 pence from 90.93 pence

Euro/dollar: DOWN at $1.2164 from $1.2244

Dollar/yen: UP at 103.60 yen from 103.32 yen

West Texas Intermediate: DOWN 2.8 percent at $47.74 per barrel

Brent North Sea crude: DOWN 2.6 percent at $50.91 per barrel