SAN FRANCISCO  Google said Wednesday that it would offer ultrahigh-speed Internet access in some communities in a test that could showcase the kinds of things that would be possible if the United States had faster broadband networks.

In Google’s vision of the future of the Internet, the live streaming of 3-D medical images from a rural health clinic to a specialized medical center or the downloading of a full-length movie in a matter of minutes would become commonplace.

But Google’s promise to build the demonstration network is also the latest example of the Internet search company using its money and industry clout to help shape the future of the Internet to its liking.

Google has long been unhappy with the state of broadband in America, where speeds lag far behind those of other developed countries. It announced the plan for its high-speed network, which would be open to other companies wanting to offer Internet service, just as federal regulators were debating new rules for the Internet and preparing a national broadband plan commissioned by Congress that could call for higher-speed networks to be available nationwide.