Japan's Nikkei 225 index shed 0.8 percent to 9,085.01, while South Korea's Kospi dropped 1.2 percent to 1,919.96. Hong Kong's Hang Seng fell 0.8 percent to 19,935.45, while Australia's S&P/ASX 200 dipped 0.2 percent to 4,373.20.
In mainland China, the Shanghai Composite Index slid 0.4 percent to 2,110.91. Benchmarks in Singapore, Taiwan and New Zealand also fell.
Provisional trade figures showed Japan posted a 517.4 billion ($6.5 billion) trade deficit in July, compared with a surplus the year before, as exports fell 8 percent. Exports of autos and electronics by Asia's second-biggest economy have been hurt by the strengthening yen as well as weak demand from Europe as it battles a debt crisis.
Investors are also awaiting developments as Greek Prime Minister Antonis Samaras meets Luxembourg Prime Minister Jean-Claude Juncker, who chairs the eurozone finance ministers' meetings, in Athens later Wednesday. Samaras is expected to request an extension of Greece's deadline to meet fiscal targets as the country carries out painful reforms.
On Wall Street on Tuesday, the Dow Jones industrial average fell 0.5 percent to close at 13,203.58 while the broader S&P 500 lost 0.
Crude oil fell 14 cents to $96.70 per barrel in electronic trading on the New York Mercantile Exchange. The contract rose 71 cents to settle at $96.68 per barrel in New York on Tuesday.
In currencies, the euro weakened slightly to $1.2464 from $1.2467 late Tuesday in New York. The dollar fell to 79.25 Japanese yen from 79.42 yen.