Asian markets rose early Tuesday, as investors shrug off twin concerns over Greece's debt situation and China's economy, which led to a plunge in oil prices.

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.

"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.

The Nikkei 225 Stock Average rose 1.5% and Australia's S&P/ASX 200 rose 1.6%, while South Korea's Kospi Composite was flat.

Nymex crude rebounded 0.8% to $52.93 in early trading after a 7.7% plunge on Monday amid fresh fears about weaker demand from China, one of the world's largest consumers of raw materials. Oil prices had their biggest single-day declines in more than three months Monday.

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 0.2% 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.

China's market volatility is starting to spill into global markets, as Beijing's aggressive efforts to rescue its falling stock prices casts more doubt on the health of the world's second-largest economy.

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.

Over the weekend, 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.

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

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