European and US stocks mostly climbed Thursday, boosted by US stimulus hopes, vaccine rollouts and upbeat news from Italy amid a calmer trading environment after last week's volatility.

Both the S&P 500 and Nasdaq finished at all-time highs, extending a strong rally this week with the ebbing of last week's buying frenzy of GameStop and other equities. Investors are increasingly confident that volatility in those equities won't dent confidence in the broader stock market.

Art Hogan, chief market strategist at National Securities, said investors have also been cheered by the drop in new US coronavirus cases and an increase in vaccination rates.

"We clearly are seeing fewer cases and fewer hospitalizations," Hogan said.

Hogan also cited improving economic data, but cautioned that much stronger data -- including in Friday's jobs report -- could bolster critics of President Joe Biden's $1.9 trillion stimulus plan.

Earlier, European markets were also broadly higher.

Milan rose by 1.6 percent after former European Central Bank chief Mario Draghi got to work on trying to form a new Italian government to lift his country out of coronavirus-induced turmoil.

"Draghi has been asked to form a government of national unity in Italy. He's a highly skilled operator, a consummate politician and we know he'll do 'whatever it takes' to steer Italy out of its worst economic and health crisis since the war," said Markets.com analyst Neil Wilson.

However, London stocks were essentially unchanged after the Bank of England held its key interest rate at a record-low 0.1 percent and stimulus levels steady, causing the pound to rise.

The BoE also cut its 2021 gross domestic product growth forecast to 5.0 percent from 7.25 percent although Britain has moved faster than most countries in its vaccination campaign.

The central bank also hinted at the possibility of negative interest rates later this year.

Among individual companies, Apple jumped 2.6 percent following reports it is close to a deal on producing its own autonomous vehicles in cooperation with South Korean giant Hyundai. Neither company commented on the reports.

Disney rose 2.2 percent after a bipartisan group California state lawmakers released legislation that would allow the state's theme park to reopen more quickly than under the current state plan.

Disney has criticized the coronavirus plan by Governor Gavin Newsom as overly restrictive.

A pick-up in vaccinations and signs that infections and deaths are slowing has lifted hopes for an easing of containment measures soon
A pick-up in vaccinations and signs that infections and deaths are slowing has lifted hopes for an easing of containment measures soon AFP / Alexander NEMENOV

New York - Dow: UP 1.1 percent at 31,055.86 (close)

New York - S&P 500: UP 1.1 percent at 3,871.74 (close)

New York - Nasdaq: UP 1.2 percent at 13,777.74 (close)

London - FTSE 100: DOWN 0.1 percent at 6,503.72 (close)

Frankfurt - DAX 30: UP 0.9 percent at 14,060.29 (close)

Paris - CAC 40: UP 0.8 percent at 5,608.54 (close)

Milan - FTSE MIB: UP 1.7 percent at 22,900.55 (close)

EURO STOXX 50: UP 0.9 percent at 3,642.12 (close)

Tokyo - Nikkei 225: DOWN 1.1 percent at 28,341.95 (close)

Hong Kong - Hang Seng: DOWN 0.7 percent at 29,113.50 (close)

Shanghai - Composite: DOWN 0.4 percent at 3,501.86 (close)

Euro/dollar: DOWN at $1.1962 from $1.2036 at 2200 GMT

Dollar/yen: UP at 105.52 yen from 105.03 yen

Pound/dollar: UP at $1.3666 from $1.3647

Euro/pound: DOWN at 87.52 pence from 88.19 pence

West Texas Intermediate: UP 1.0 percent at $56.23 per barrel

Brent North Sea crude: UP 0.7 percent at $58.84 per barrel