BEIJING/LONDON - China warned on Monday that trade talks with the United States were "impossible" under current conditions after President Donald Trump reassured markets by suggesting that the dispute could be resolved.

The two sides have announced tit-for-tat tariffs and threatened to hit each other with more duties, raising the prospect of a trade war that could rattle the global economy.

Asian markets rose on Monday after Trump tweeted that he saw an end to the escalating dispute before the higher tariffs threatened on hundreds of billions of goods would come into effect. But China's foreign ministry was less sanguine.

"Up to now, Chinese and US officials have not held any negotiations on the trade dispute," foreign ministry spokesman Geng Shuang told reporters during a regular press briefing.

"Under the current conditions, it is impossible for the two sides to have any negotiations on this issue," Geng added.

A few hours later, Trump returned to tougher talk with an early-morning tweet railing against China's duties on US cars.

"When a car is sent to the United States from China, there is a Tariff to be paid of 2 1/2%. When a car is sent to China from the United States, there is a Tariff to be paid of 25%," Trump tweeted.

"Does that sound like free or fair trade. No, it sounds like STUPID TRADE -- going on for years!"

Trump had sounded an optimistic tone on Sunday, playing up his personal relationship with Chinese President Xi Jinping.

"President Xi and I will always be friends," Trump tweeted.

"China will take down its trade barriers because it is the right thing to do."

The president's remarks came weeks after his decision to tax imports of steel and aluminium, followed by planned levies on $50 billion worth of goods from China over what Washington says is theft of intellectual property and technology. China retaliated by unveiling planned levies on $50 billion worth of major US exports, including soybeans, cars and aircraft.

Trump then threatened to impose more tariffs on $100 billion worth of Chinese goods, prompting Beijing to warn that it would stand firm and punch back with great strength.

Trump's moves, part of his protectionist "America First" agenda, have given investors the jitters, fearing a trade war between the world's top two economies could reverse a tentative global recovery. US officials have worked to reassure the business community, though messaging has been mixed and financial markets have roiled.

In TV appearances, Trump's top economic advisor Larry Kudlow has often suggested the tariffs might not go into effect but also warned Friday they were not just a "negotiating card".

US Treasury Secretary Steven Mnuchin said the White House hoped to negotiate but acknowledged a trade war was a possibility.

Meanwhile, world markets were mostly firmer Monday as fears about a China-US trade war were tempered by hopes the two sides will be able to come to an understanding, dealers said.

Asian and European equities rebounded somewhat, despite heavy pre-weekend losses on Wall Street, as trade war fears gave way to moderate investor optimism -- but doubts remained.

"European markets are in a more optimistic mood today, with the focus shifting towards a more constructive end to the US-China stand-off," said analyst Joshua Mahony at trading group IG.

"However, recent weeks have shown us that volatility is likely to remain a key part of the trading landscape, with daily shifts in tone from US and China driving huge swings in stocks of late."

US stocks pared Friday's losses at the opening bell on Monday, rising 0.7 percent.

They plunged around two percent Friday after Donald Trump warned of tariffs on an additional $100 billion worth of Chinese imports, to which Beijing responded by saying it would stand firm.

The president's announcement came weeks after his decision to tax imports of steel and aluminium, followed by planned levies on $50 billion worth of goods from China over what Washington says is theft of intellectual property and technology.

China retaliated by unveiling planned levies on $50 billion worth of major US exports.

Trump's moves, part of his protectionist America First agenda, have rattled world markets, fearing a trade war between the world's top two economies could reverse the tentative global recovery.

"Much ink has been spilt over trade wars in the last few days, and we now wait to see what the Trump administration does next," said Stephen Innes, head of forex trading for Asia Pacific at OANDA.

There are hopes Trump's headline-grabbing tariffs are part of a plan to take a harsh line as a bargaining tactic towards a deal with China.

And on Sunday, Trump tweeted that he saw an end to the dispute, saying: "China will take down its trade barriers because it is the right thing to do."

- Russian assets tank -

However top advisor Larry Kudlow, who has often suggested the tariffs might not go into effect, warned Friday the announcements were not negotiating tactics, while Treasury Secretary Steven Mnuchin said the White House hoped to negotiate but acknowledged a trade war was a possibility.

Investors will be keeping a close eye on comments Tuesday by Chinese President Xi Jinping at the Boao Forum -- dubbed the Asian Davos -- to see if he comments on the brewing row.

Chinese foreign ministry spokesman Geng Shuang on Monday told reporters that trade talks with the US were "impossible" under current conditions.

Russian assets, meanwhile, tanked following a new round of US sanctions targeting President Vladimir Putin's oligarch allies and their companies as well as senior officials.

Shares in Russian aluminium giant Rusal collapsed, losing nearly 50 percent and putting the metals major at risk of defaulting on part of its debt.

The ruble fell by just under three percent against the dollar, while Moscow's stock market indices tumbled by around 10 percent.