Trump said he had approved the deal in New Jersey late last week, Taipei-based Central News Agency reported on Monday.
Trump was dismissive of Obama's speech.
Trump has made addressing illegal immigration a key facet of his presidency.
Trump did not specifically reference the plan during a speech to veterans in Kansas City, but asked for patience as he attempts to renegotiate trade agreements that he said have hurt American workers.
Tsai Ing-wen, the leader of Taiwan's ruling Democratic Progressive Party, refused to recognize the one-China principle as she started her second term as Taiwan leader last week.
Trump and Tillerson are "going to work together to close out what we've seen to be an incredible year", Sanders said.
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Tsang Kwok-wai was appointed the Director of Immigration.
Trump and his wife also were to pay their respects at a Pentagon ceremony led by Defense Secretary Jim Mattis and Gen. Joseph Dunford, chairman of the Joint Chiefs of Staff. The observances come as Trump grapples with the death and destruction caused by two hurricanes in three weeks.
Trump has accepted Xi's invitation to visit China this year. Chinese officials have said that Beijing is ready to work with Washington to ensure that Trump's visit yields positive outcomes.
Trump's announcement has sent shock waves across Congress, triggering strong pushback, especially from Democrats.