Asian shares were mixed in a muted reaction Tuesday to the inauguration of U.S. President Donald Trump. U.S. markets were closed Monday for the Martin Luther King Jr. Day holiday. U.S. futures rose and oil prices declined.

Asian stocks have retreated after U.S. stocks fell as good news on the job market raised worries over inflation.

Sentiment also was helped by upbeat comments by U.S. and Chinese officials ahead of President-elect Donald Trump's inauguration later Monday. Pledges by both sides to work to improve relations may have alleviated some concerns over trade tensions that have built up as businesses brace for a possible increase in tariffs on Chinese exports to the U.