China's blue chip index edged up 0.1% at the open, as Hong Kong's Hang Seng Index gained 0.44%.
The future of Evergrande, the world's most indebted property developer, is being forensically scrutinised by investors after the company last Friday did not meet a deadline to make an interest payment to offshore bond holders.
Evergrande has 30 days to make the payment before it falls into default and Shenzen authorities are now investigating the company's wealth management unit.
Without making reference to Evergrande, the People's Bank of China (PBOC) said Monday in a statement posted to its website that it would "safeguard the legitimate rights of housing consumers".
Widening power shortages in China, meanwhile, halted production at a number of factories including suppliers to Apple Inc and Tesla Inc and are expected to hit the country's manufacturing sector and associated supply chains.
Analysts cautioned the ongoing blackouts could affect the country's listed industrial stocks.
"What we see in China with the developers and the blackouts is going to be a negative weight on the Asian markets," Tai Hui, JPMorgan Asset Management's Asian chief market strategist told Reuters.
"Most people are trying to work out the potential contagion effect with Evergrande and how far and wide it could go. We keep monitoring the policy response and we have started to see some shift towards supporting homebuyers which is what we have been expecting."
On Wall Street, the Dow Jones Industrial Average rose 144.36 points, or 0.41%, to 34,942.36, the S&P 500 lost 4.57 points, or 0.10%, to 4,450.91 and the Nasdaq Composite dropped 68.29 points, or 0.45%, to 14,979.41.
Rising bond yields prompted a shift from growth to cyclical stocks in the United States, in a move that analysts expect could become more permanent after a prolonged period of supressed bond yields.
U.S. Treasury yields soared to a three-month high, touching 1.516% overnight following the Federal Reserve's move last week to indicate fiscal stimulus could be tapered as early as November.
U.S. investors are looking ahead to speeches later this week from several senior Fed officials, as well as keeping an eye on any developments at China Evergrande, broker Ord Minnett said in a note.
In Asian trade, the dollar was up nearly 0.1% in line with its performance in the international session Monday after it rose alongside bond yields.
Gold was flat, while Brent crude oil was down 0.2%.
(Reporting by Scott Murdoch; editing by Richard Pullin) ((Scott.Murdoch@thomsonreuters.com;))
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