Asian shares were lower on Monday as investors eye the international backlash against U.S. President Donald Trump's immigration policy, which has added pressure on the dollar.

Several countries have criticized President Trump's latest executive order to block refugees from seven predominantly Muslim countries from entering the United States for a four-month period. Several attorney generals from California, New York, Washington DC and 13 other states have pledged to fight the "unconstitutional" move, Reuters reported.

Trump defended his actions late Sunday, saying that it was about national security and not religion.

The dollar index, which tracks the greenback against a currency basket, was at 100.18 versus levels above 100.50 seen late last week after the Dow Jones industrial average rose above 20,000.

"Whether the markets start to price in a stronger Trump risk premium is yet to be seen, but the S&P 500 rallying 1 percent last week in the face of various protectionist measures suggest this premium is not yet in the market," said Chris Weston, chief market strategist at spread-better IG, in a note on Monday.

U.S. futures were all in the red during Asian trade. Dow Jones futures were down 0.23 percent, Nasdaq futures slipped 0.3 percent and S&P 500 futures were off 0.31 percent.