WASHINGTON—Some White House officials view next-generation 5G wireless service as a “key area of competition,” and they say that the threat from China, in particular, justifies a “moonshot” government effort like the construction of the interstate highway system, an internal memo shows.

The memo—produced by officials at the National Security Council—urges the Trump administration to consider extraordinary efforts to clear the way for the new technology or even to help build it in order to counter the growing economic and political...