Trump has had a rocky relationship with the 28-nation military alliance. As a candidate, he called NATO "obsolete."
The president has criticised several members of the post-World War II organisation for not spending adequately on defence. At a May meeting in Brussels with NATO members, Trump complained that his allies had shortchanged "the people and taxpayers of the United States," creating additional strains for the organisation.
Hutchison, who is 73, won a runoff special election to fill a vacant Senate seat in 1993 and served three full terms.