(Reuters) - Asian stocks came under pressure on Friday as investors sought safe havens, such as the U.S. dollar, fearing that a resurgence in coronavirus cases and a lack of additional U.S. fiscal stimulus would hobble the world economy. U.S. President Donald Trump’s offer on Thursday to raise the size of a fiscal stimulus package to win the support of Republicans and Democrats helped narrow Wall Street losses, though many investors still believe a deal is unlikely before the Nov. 3 election. “There’s a bit of worry there and also at what we’re seeing in America and in Europe regarding the virus and how it seems to be taking hold pretty significantly again,” said Grant Williamson, investment adviser at Hamilton Hindin Greene in Christchurch, New Zealand. Stocks struggled to make gains in early Asian trade with Australia"s S&P/ASX 200 .AXJO down 0.02% and Japan"s Nikkei 225 futures NKc1 adding just 0.06%. Hong Kong"s Hang Seng index futures .HSIHSIc1 rose 0.36%. E-mini futures for the S&P 500 EScv1 rose 0.04%. Australia and New Zealand investors were likely to “take a breather” on Friday, especially after New Zealand equities climbed 6% during October, Williamson said. On Wall Street, the Dow Jones Industrial Average .DJI fell 0.07%, the S&P 500 .SPX 0.15% and the Nasdaq Composite .IXIC dropped 0.47%. An unexpected rise in U.S. weekly jobless claims figures added to worries about a sputtering world economy, especially in the face of a spike in COVID-19 cases in Europe. Safe-haven demand due to signs of a stalling U.S. economy drove the dollar index =USD 0.398% higher after touching a two-week high of 93.91, while the Japanese yen strengthened 0.08% versus the greenback at 105.38 per dollar. MSCI"s broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS closed 0.04% lower. The euro EUR= was down 0.01% to $1.1705, while a firmer U.S. dollar dragged on sterling GBP=, which was last trading at $1.2902, down 0.09% on the day. Spot gold XAU= was little changed at $1,908.07 an ounce. Focus in Asia swings to Canada-China relations after Canada ordered a national security review of Shandong Gold Mining Co Ltd"s 600547.SS1787.HK bid to acquire a gold mine in the Canadian Arctic. It is the latest sign of pushback faced by China"s state miners. In Europe, London will enter a tighter COVID-19 lockdown from midnight on Friday as Prime Minister Boris Johnson seeks to tackle a swiftly accelerating second coronavirus wave. “The market’s on again off again love affair with an impending stimulus torrent masks the fact that investor uncertainty is bristling ahead of an expected choppy period in terms of headline risk, including Brexit, the U.S. election, and perhaps the most horrifying troubles of all, the second wave of the coronavirus that could trigger more intense lockdown worries,” said Stephen Innes, global chief market strategist at AxiCorp. Brexit talks continued as The European Union put the onus on Britain on Thursday to compromise on their new economic partnership or stand ready for trade disruptions in less than 80 days. Britain’s Brexit negotiator, David Frost, said on Twitter he was “disappointed.” The Australian dollar fell 0.06% versus the greenback at $0.709. Oil prices were weighed by concerns about the coronavirus and its impact on the world economy. Brent crude futures LCOc1 dropped 16 cents to settle at $43.16 a barrel, while U.S. West Texas Intermediate crude futures CLc1 slipped 8 cents to settle at $40.96 a barrel. Traders" preference for safety helped government bonds. The yield on U.S. Treasuries Benchmark 10-year notes US10YT=RR was last 0.7306% from 0.734%.