He enlisted in the Navy in 1998.
White House press secretary Sean Spicer said there are no guarantees it will happen.
The president offered few details on how the program or contract would change as a result.
'This spits in the face of almost 16 years of cooperation with Muslim allies," said one former soldier.
Three other U.S. troops were wounded in the operation on Saturday against members of al-Qaeda in the Arabian Peninsula.
Trump said he will defer to Defense Secretary Jim Mattis, who is against torture, on how the U.S. handles interrogations.
In a memo, Defense Secretary retired Gen. James Mattis ordered the deputy defense secretary to initiate reviews.
President Trump's interactions with senior military leaders may shed new light on his approach to issues of national security.
A proposed executive order that would reduce the number of immigrants and refugees from certain countries will likely affect thousands of Iraqis who helped the American military and have applied for visas to come to the United States, according to refugee and immigrant advocacy groups.
The Defense Department was 'preyed upon by the trolls of the Internet,' a Pentagon spokesman said.
