LONDON/SINGAPORE - European and Asian shares rose on Tuesday after US President Donald Trump touted possible tariff changes on autos, while US Treasuries steadied having staged a recovery the day before following last week's historic selloff.

Trump said on Monday he was considering a modification to the 25 percent tariffs imposed on foreign auto and auto parts imports from Mexico, Canada and other places.

That followed Friday's move to exempt smartphones, computers and some other electronics from Trump's "reciprocal" tariffs.

"Markets have been itching for any signs of positivity," said Dan Boardman-Weston, CEO and CIO at BRI Wealth Management.

"The announcement about electronics and phones over the weekend was helpful for sentiment and you've seen markets rally a bit in the last few days."

Investors took whatever good news they could get after the recent heavy selling across markets, and pushed shares higher.

The pan-European STOXX 600 index rose 0.8 percent on Tuesday, led by the autos and parts sector whose gauge jumped 2.6 percent.

Germany's DAX rose 1.3 percent and Britain's FTSE 100 index jumped 0.8 percent. France's CAC 40 was little changed, weighed by the luxury sector after disappointing earnings from LVMH.

In Asia, MSCI's broadest index of Asia-Pacific shares outside Japan was up 1 percent.

Japan's Nikkei rose 0.8 percent, with shares of auto companies like Toyota and auto parts maker Denso among the top gainers.

"When we start to see some of these exemptions flow through for particular sectors, it helps markets think about tariffs as something that aren't necessarily going to be all-encompassing, and that they might actually be reprieved," said Illiana Jain, an economist at Westpac.

Analysts remained cautious, however, as uncertainty over Trump's trade policies, and his constant back-and-forth on tariffs, continued to cast a cloud over markets and the global economic outlook.

US futures swung between losses and gains to last trade marginally higher after Monday's advance on Wall Street, its second straight daily rise for the first time since Trump announced his reciprocal tariff plan on April 2.

Nasdaq futures rose 0.4 percent and S&P 500 futures were up 0.3 percent.

Investors have more earnings to weather this week with Bank of America and Citigroup among the big banks reporting. Numbers from chipmaker TSMC later in the week will also be a highlight.

Bond yields steady

US Treasuries held onto Monday's gains on Tuesday after a manic selloff last week that led to the largest weekly increase in borrowing costs in decades. Bond yields move inversely to prices.

The benchmark 10-year yield was up 1 basis point (bp) at 4.372 percent, having fallen nearly 13 basis points in the previous session.

The two-year yield was up about 3 bps at 3.862 percent after sliding 12 bps on Monday.

Some analysts said comments from Federal Reserve Governor Christopher Waller contributed to the fall in yields.

He said on Monday that the Trump administration's tariff policies were a major shock to the US economy that could lead the Fed to cut rates to head off recession even if inflation remained high.

Atlanta Fed Bank President Raphael Bostic, meanwhile, suggested the US central bank should stay on hold until there is more clarity.

Markets are now pricing in about 83 bps worth of monetary policy easing by the end of the year, with most expecting the Fed to hold rates next month.

In currencies, the euro was close to its three-year peak against the dollar at $1.1362, as the US unit remained under pressure.

The dollar was near its recent 10-year low against the Swiss franc and fell to a more than six-month low against the pound.

"(The) behaviour of the US dollar recently has changed – it is now ignoring rate differentials, and responding more to capital flows," said Bharat Sachanandani, head of flow strategy and solutions for Asia Pacific at Societe Generale.

"The US dollar is not liking the prospect of US corporations being less profitable, US consumers facing higher inflation and foreign investors having a collapsing appetite for US assets."

Oil prices rose, boosted by the latest tariff exemptions floated by Trump. Brent crude futures gained 0.5 percent to $65.22 per barrel, while US crude was up 0.6 percent at $61.87.

Spot gold rose 0.5 percent to near its record high at $3,226 an ounce.