Stock markets rose Tuesday as auto firms were boosted by US President Donald Trump's suggestion of flexibility over steep tariffs on the sector. 

Some stability has returned to markets after last week's rollercoaster ride over Trump's stop-start tariff announcements, but uncertainty remains over speculation of new levies on high-end technology and pharmaceuticals.

European indices were higher, tracking gains in Asia, with London up 0.8 percent and Frankfurt climbing around one percent around midday.

Paris made more modest gains, weighed by shares in luxury conglomerate LVMH falling more than seven percent after it reported a decline in sales. 

The auto sector rallied following Trump's comments on Monday that he was "very flexible" and "looking at something to help some of the car companies" hit by his 25 percent tariff on all imports.

"This serves to double down on the weekend narrative that Trump will reverse some of his tariffs once company execs approach him to highlight the huge negative implications of his action," said Joshua Mahony, chief market analyst at Scope Markets. 

"It therefore comes as no surprise to see the likes of Aston Martin Lagonda, BMW, and Volkswagen heading up the gainers," he added.

Automaker Stellantis, whose brands include Jeep, Fiat and Peugeot, gained over four percent in Paris, while German brands Volkswagen and Mercedes-Benz advanced more than two percent. 

In Asia, Toyota jumped 3.7 percent and Hyundai more than four percent.

Markets made a positive start to the week, rising the previous day after the announcement of tariff exemptions for consumer electronic products, though Trump's suggestion that the reprieve would be temporary tempered the optimism.

"Sentiment got a further boost thanks to positive noises about trade negotiations, which added to the sense that the administration is focused on making deals that could see the tariffs come down," said Jim Reid, analyst at Deutsche Bank.

Treasury Secretary Scott Bessent said Monday that a China-US deal could be done, in an apparent olive branch as the two economic powerhouses trade tariff threats.

Trump has hammered China with duties of up to 145 percent, while Beijing has imposed retaliatory measures of 125 percent.

Other countries are negotiating with Washington.

Trump aide Kevin Hassett said the White House had received "more than 10 deals where there's very, very good, amazing offers made to us", but did not specify from which countries they came.

After a broadly positive day on Wall Street, Asian markets pushed higher, with Tokyo, Hong Kong, Seoul and Shanghai all rallying.

And South Korea's announcement of plans to invest an additional $4.9 billion in the country's semiconductor sector gave a little lift to chip giants Samsung and SK hynix.

Federal Reserve governor Christopher Waller provided some support to markets after suggesting he would back the central bank to cut interest rates to help the economy, instead of focusing on higher inflation.

Key figures around 1100 GMT

London - FTSE 100: UP 0.8 percent at 8,199.98 points

Paris - CAC 40: UP 0.3 percent at 7,292.32

Frankfurt - DAX: UP 1.0 percent at 21,163.50 

Tokyo - Nikkei 225: UP 0.8 percent at 34,267.54 (close)

Hong Kong - Hang Seng Index: UP 0.2 percent at 21,466.27 (close)

Shanghai - Composite: UP 0.2 percent at 3,267.66 (close)

New York - Dow: UP 0.8 percent at 40,524.79 (close)

Dollar/yen: DOWN at 142.89 yen from 143.09 yen on Monday

Euro/dollar: DOWN at $1.1344 from $1.1356 

Pound/dollar: UP at $1.3244 from $1.3189

Euro/pound: DOWN at 85.64 pence from 86.08 pence

West Texas Intermediate: DOWN 0.3 percent at $61.36 per barrel

Brent North Sea Crude: DOWN 0.3 percent at $64.69 per barrel