The Tokyo Stock Exchange's benchmark Nikkei lost 0.9 percent to 9,003.19. South Korea's Kospi index lost 0.3 percent to 1,912.42. Key indexes were also down in Singapore, Indonesia and
Taiwan. Mainland Chinese shares were mixed, while benchmarks in New Zealand, Thailand and Australia rose.
Nobuhiko Kuramochi, head of the investment information department at Mizuho Securities Co. in Tokyo, said that traders were not going to make major moves ahead of key events later in the week, including U.S. Federal Reserve Chairman Ben Bernanke's speech in Wyoming.
Traders were also looking ahead to the release of U.S. April-June gross domestic product data set for Wednesday.
"Attention is on how overseas markets are faring as those herald major risks," Kuramochi said. "With Japanese exports already declining, they will determine the momentum of manufacturing issues."
Also weighing on sentiments was a monthly Japanese government report on the economy, released Tuesday, whose language on the main assessment was changed—to a more pessimistic one, for the first time in 10 months—to highlight concerns about weaknesses, stemming from dwindling exports.
Among issues, Sharp Corp., a troubled Japanese electronics maker, which has nose-dived over the last several months sessions, recouped nearly 5 percent amid expectations it will gain some cash.
Olympus Corp., another troubled electronics maker, inched up 0.5 percent after announcing it was selling a telecommunications subsidiary earlier this week.
In Seoul, shares of Samsung Electronics rose 1.6 percent, clawing back some of the value lost on Monday, when the stock plunged 7.5 percent in reaction to a U.S. court order that Samsung pay rival Apple $1 billion in damages for illegally copying its products.
Stock markets in London were closed Monday for a bank holiday, dampening trading activity.
Overnight, Wall Street remained subdued, awaiting signals from the Fed about possible help for the economy.
The Dow Jones industrial average fell 0.3 percent to 13,124.67. The Standard & Poor's 500 Index fell 0.69 point, or 0.05 percent, to 1,410.44. The Nasdaq composite index rose 0.1 percent to 3,073.19.
Investors are waiting on prospects for more economic stimulus from central banks in China and the U.S. and a financial stability plan from the European Central Bank.
Economists have been warning the debt crisis in the 17-country eurozone could eventually catch up with Germany. Troubles elsewhere are starting to make themselves felt. Italy and Spain, the No. 3 and No. 4 eurozone economies, are in recessions as they try to reduce budget deficits and struggle to refinance their debts in bond markets.
So far, exports of cars and industrial machinery to stronger economies in Asia and the U.S. have helped Germany grow, while low unemployment has buoyed consumer spending at home. But those advantages may not be enough for much longer against the undertow from the eurozone crisis.
Benchmark oil for October delivery fell 5 cents to $95.42 per barrel in electronic trading on the New York Mercantile Exchange. The contract fell 68 cents to close at $95.47 on the Nymex on Monday.
In currencies, the euro fell to $1.2484, down from $1.2503 late Monday in New York. The dollar fell to 78.50 yen from 78.75 yen.