Japan's benchmark Nikkei 225 stock average lost 24.07 points, or 0.2 percent, to 10,516.97 in the morning session. China's Shanghai Composite Index edged down 0.2 percent to 2,785.77. South Korea's Kospi declined 0.4 percent to 2,073.47.

Sentiment was sluggish across Asia amid growing speculation that Portugal would be forced into a bailout, joining Greece and Ireland in getting massive financial help from its European partners and the International Monetary Fund.

Portugal is to sell bonds on Wednesday, with Italy and Spain scheduled to sell bonds later in the week. If the sales go poorly, it could further weaken confidence in Europe's financial system.

Elsewhere, shares in Australia, Malaysia and Singapore were lower. But Hong Kong's Hang Seng index edged up 0.2 percent to 23,565.46.

Stocks in New Zealand and Taiwan were slightly higher.

The European debt crisis also pressured U.S. stocks with the Dow Jones industrial average losing 37.31 points, or 0.3 percent, to 11,637.45 on Monday, falling for the third straight day.

In currencies, the dollar rose to 83.01 yen in Tokyo from 82.69 yen in New York late Monday. The euro climbed to $1.2955 from $1.2947.

Benchmark oil for February delivery was up 10 cents to settle at $89.35 a barrel on the New York Mercantile Exchange.