WASHINGTON — The Trump administration is divided over how aggressively to restrict China’s access to United States technology as it looks for ways to protect national security without undercutting American industry.

President Trump and many of his top advisers have identified China’s technological ambitions as a national security threat and want to limit the type of American technology that can be sold overseas. But a plan to do just that has encountered stiff resistance from some in the administration, who argue that imposing too many constraints could backfire and undermine American industry.

The debate underscores the extent to which Mr. Trump’s trade fight with China has left many issues unresolved. The president announced plans this month to sign a “Phase 1” trade agreement that would require China to buy more farm products and agree to some technology protections in exchange for a pause in new American tariffs.

The agreement, which has yet to be signed, lowered tensions between the two nations. But concerns about Beijing’s economic ambitions remain, posing an even greater challenge as the United States considers what steps to take to ensure American companies dominate the next generation of technologies.