Chinese equities firmed as some investors took advantage of cheap share prices. The Shanghai Composite gained 0.1% and the blue-chip CSI 300 rose 0.4% in afternoon trade. Hong Kong's Hang Seng added 0.3%.
Japan's Nikkei average was lower by 0.3%.
On Wall Street, the Dow Jones Industrial Average fell 1.1%, the S&P 500 lost 1.2% and the Nasdaq Composite dropped 1.6%, as traders dumped cyclical names on fears that the escalating U.S.-China trade war would stymie global economic growth.
U.S. President Donald Trump said on Thursday that Washington's complaints against Huawei Technologies might be resolved within the framework of a U.S.-China trade deal, while calling the Chinese telecom giant "very dangerous."
Jasper Lawler, head of research at London Capital Group, said "the fact that Trump is still talking about a trade agreement is offering some optimism to the markets."
"Traders have been focused on the damage to the global economy that a prolonged trade war could cause, so a break from the bad news is cautiously lifting sentiment," he wrote in a note on Friday, commenting on the expected higher European open.
Washington last week effectively banned U.S. firms from doing business with Huawei, the world's largest networking gear maker, citing national security concerns.
The U.S. Commerce Department said on Thursday it was proposing a new rule to impose anti-subsidy duties on products from countries that undervalue their currencies, in another move that could penalise Chinese products.
China's Commerce Ministry hit back on Thursday, with its spokesman saying "if the United States wants to continue trade talks, they should show sincerity and correct their wrong actions."
Masanari Takada, cross-assets strategist at Nomura Securities in Tokyo, said the U.S.-China trade conflict "has not yet fully dented the global investor sentiment, so there is no panic-selling. But at the same time, the sentiment will likely remain weak."
As flight-to-safety plays dominated global markets, the benchmark 10-year U.S. Treasury note yield hit 2.292%, the lowest level since mid-October 2017, with the key parts of the yield curve inverted. The yield last stood at 2.3237%.
Chotaro Morita, chief fixed income strategist at SMBC Nikko Securities, said big falls shown in a fresh U.S. manufacturing survey appear to reflect expectations of a breakdown in the U.S-China trade talks.
"In the last couple of years, the PMI has had a very small gap with hard data, such as industrial output. So if that holds true this time, we could see factory production plunging into negative levels (compared to a year ago)."
"Since the global financial crisis, U.S. output has fallen only once: from 2015 to early 2016 when the shale industry was badly hit. Markets could start to fret over a global slowdown as they have done late last year."
The dollar index, which measures it against six major currencies, hit a high of 98.371 on Thursday U.S. time. It was last quoted at 97.847, little changed on the day.
The euro on Thursday slumped to levels last seen in May 2017 as a recovery in euro zone business activity was weaker than expected. Early Friday, the currency was flat on the day at $1.1181.
Sterling weakened again on Thursday as pressure mounted on British Prime Minister Theresa May to name a date for her departure after a backlash over her last-ditch plans for Britain's exit from the European Union.
The pound was last traded at $1.2663, little changed on the day. Sterling suffered its 14th consecutive day of losses against the euro on Thursday, its longest losing streak on record. It stood at 0.8829 pound to the euro.
Other major currencies were relatively calm. The dollar was holding at 109.59 yen, flat on the day.
In commodity markets, oil prices tumbled on Thursday as trade tensions dampened the demand outlook, with the crude benchmarks posting their biggest daily falls in six months.
Oil prices stabilised on Friday amid OPEC supply cuts and tensions in the Middle East.
U.S. crude was last seen at $58.58 a barrel, up 1.16%, after Thursday's 5.7% fall that took it to the lowest in two months. Brent crude futures rebounded 1.18% to $68.56 per barrel, after falling 4.6% in the previous session.
(Additional reporting by Hideyuki Sano in Tokyo; Editing by Sam Holmes and Simon Cameron-Moore) ((Noah.Sin@thomsonreuters.com; +852 2841 5782; Reuters Messaging: firstname.lastname@example.org; Twitter: https://twitter.com/noah_sin))
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