By Gregor Stuart Hunter 

China's stocks fell early Tuesday, casting doubt on the potency of Beijing's aggressive rescue efforts, while investors elsewhere in Asia appear to shrug off concerns over Greece's debt situation.

The Shanghai Composite is down more than 3%, wiping out a rebound on Monday. The Shenzhen Composite fell 3.4% while the ChiNext board, composed of smaller cap stocks, and sank 4.2%. All indexes are off more than a quarter from June highs.

Stocks in Hong Kong recovered after their biggest fall in three years on Monday, with the benchmark gaining 0.6%. A gauge of Chinese companies with Hong Kong listings, known as H-shares, was flat.

China has rolled out a steady stream of measures to arrest the selling frenzy that knocked $2.4 trillion in value from China's equities over the past three weeks. Shanghai recovered modestly Monday, which some investors and analysts attributed to heavy buying of blue-chip stocks by state-backed funds. Despite the recent rout, Shanghai shares are up 82% over the past year, and 16% since January.

Yet China's volatility is starting to spill into global markets, as Beijing's moves to arrest stock selloffs have darkened the outlook for the world's second-largest economy. Oil prices tumbled nearly 8% Monday, their biggest single-day decline in more than three months, amid fresh fears about weaker demand from China, one of the world's largest consumers of raw materials. Nymex crude rebounded 0.8% to $52.93 in early trading Tuesday.

Over the weekend, Chinese brokerages, mutual-fund managers and an investment arm of the government committed to buying stocks, while new initial public offerings were halted. Quotas for foreigners to buy stocks were increased and the central bank pledged to provide funds to help investors borrow to buy shares.

Elsewhere, Asian markets rose early Tuesday as investors appear hopeful that a resolution between Greece and its creditors is still within reach.

"It seems that investors either believe that 'Grexit' can still be avoided, or that, if it does happen, the contagion will be limited," analysts from Capital Economics wrote in a research report.

Greece's vote on Sunday to reject creditors' demands, including pension cuts and tax increases, could put Greece closer to exiting the eurozone. That led markets in Europe and the U.S. lower, though the declines weren't as dramatic as expected. The euro is unchanged against the U.S. dollar, while the yen gained 0.1% against the dollar.

The Nikkei 225 Stock Average rose 1.3% while South Korea's Kospi Composite was flat.

Australia's S&P/ASX 200 rose 1.8% with falling oil seen to lower operating costs for energy-intensive commodity producers. Traders also await an interest-rate decision from the Reserve Bank of Australia, which is expected to remain on hold.

Meanwhile, banks warned that Malaysia's financial markets could see further stress, after the country's currency fell to its lowest level this month since its peg to the U.S. dollar ended in 2005. Malaysian markets have been under pressure this year as the oil-exporting nation is hit by falling commodity prices, which have nearly halved since July last year.

"Among Asian financial assets, Malaysia's are the most exposed to oil," analysts from ING wrote in a research note. Efforts to strengthen the ringgit "will give way if oil prices continue to decline," the bank added.

The ringgit is up 0.4% against the U.S. dollar after hitting lows of 3.8260 earlier Tuesday.

Malaysia's currency also has come under pressure as political strain builds against the country's prime minister. The Wall Street Journal earlier reported that Malaysian government investigators looking into the activities of state investment fund 1Malaysia Development Bhd., or 1MDB, had traced almost $700 million in deposits into what they believe are Mr. Najib's personal accounts. Mr. Najib has denied wrongdoing.

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