By Gregor Stuart Hunter 

Chinese markets faced a volatile start to trading on Tuesday morning as a selloff deepened in small-cap stocks, as other markets in Asia shrugged off concerns about a Greek default.

The Shanghai Composite fell as much as 1.5% at the open, then veered between gains and losses, a day after a selloff that thrust the benchmark into a bear market, defined as a loss of more than 20% from its high reached on June 12. The index was last down 0.7%

Chinese authorities have tried to draw a line under the declines. The central bank cut interest rates over the weekend and late Monday the Finance Ministry announced that the state's pension fund could be allowed to invest up to 30% of its net asset value in securities

The smaller Shenzhen market fell 2.9% with the ChiNext board, which is composed of small-cap companies, down 3.9% after losing more than a third of its value from its peak earlier this month.

With investor confidence likely to remain fragile, ING said investors should watch for weakness in China spilling over into other markets.

"Controls on capital flows insulate China's financial markets from contagion due to volatility in global financial markets," analysts from ING wrote in a research note. "The controls don't insulate global financial markets from contagion emanating from China."

In Hong Kong stocks rebounded, with the Hang Seng Index up 0.4%, while listings of Chinese companies, known as H-shares, rose 0.7%.

Japan's Nikkei 225 Stock Average rose 0.5% in early trading while the S&P/ASX 200 index gained 0.2% as the effects of a market rout in the U.S., with the S&P 500 sinking 2.1%, seeming to abate.

The euro recovered slightly from a selloff on Monday, rising 0.2% to 1.1197 against the dollar even as Greece looks set to default on its payment to the International Monetary Fund due Tuesday. Still, it fell 0.3% against the Japanese yen in early Asian trade as investors seek safer assets.

The market appears "to be placing its faith in the [European Central Bank] to 'do whatever it takes' to protect the euro, whatever the outcome in Greece," says BNZ foreign-exchange strategist Kymberly Martin.

Rebecca Howard contributed to this article.

Write to Gregor Stuart Hunter at gregor.hunter@wsj.com