Tokyo shares fell while the stock market rose in Paris, Frankfurt, and Shanghai.
The uncertainty about what the Chinese government might do, if any, to reduce the potential impact of a default has rattled markets.
Evergrande is one of China's largest private sector conglomerates. It said that it would make a payment due on Thursday for a 4 billion Yuan ($620 Million) bond, which was denominated Chinese yuan.
The company statement did not indicate whether this meant that the payment would be changed. The interest rate on the bond is 5.8%, which would mean that the normal amount due for the year would be 232 million Yuan ($36 Million).
Evergrande did not provide any information about future payments, including a bond in U.S. Dollars in March.
"Evergrande is still in technical default by the banks, but the silence from Beijing is increasing market nervousness," Venkateswaran Lavandya, Mizuho Bank commented in a commentary.
Germany's DAX rose 0.6% to 15,444.30, while the CAC 40 in Paris rose 1.2% to 6,630.19. The FTSE 100 rose 0.9% to 7,042.98 in London. The contract for Dow industrials rose 0.6%, and U.S. futures rose as well. Futures for the S&P 500 rose 0.4%
The 10-year Treasury yield was stable at 1.33%, an increase of 1.32% as of Tuesday night.
Tokyo's fall in Asia was offset by the fact that other regional benchmarks were generally higher, reducing early losses.
Tokyo's Nikkei225 index fell 0.7% to 29,639.40, while Shanghai Composite index rose 0.4% to 3,628.49. The S&P/ASX 200 index in Australia gained 0.3% to 7,296.90. The shares fell by 2% in Taiwan, and they also dropped in Singapore. However, benchmarks rose in India and Indonesia as well as Malaysia.
For holidays, markets in South Korea and Hong Kong were closed
The Federal Reserve will send out its strongest signal yet this week to say it will begin reining in ultra-low-interest rates later this year. This is the first step towards removing the incredible support it has given the economy since the pandemic 18 months ago.
Wednesday's Fed policy meeting could be the beginning of a November pullback announcement.
After Monday's selloff, Tuesday saw nerves seem to be steady.
The S&P 500 fell 0.1%, while the Dow Jones Industrial Average dropped 0.1%.
The Nasdaq composite rose 0.2% and small-company stocks also saw gains. The Russell 2000 index rose 0.2%.
U.S. benchmark crude oil traded at $1.04-$71.53 per barrel on electronic trading on New York Mercantile Exchange. On Tuesday, it gained 35 cents to $70.49
Brent crude oil, which is the international standard for pricing, increased 98c to $75.34 per barrel.
Late Tuesday, the U.S. dollar rose from 109.23 to 109.42 yen to 109.42 yen. From $1.1726, the euro rose to $1.1732.