WASHINGTON — The Obama administration, resolving years of internal debate, is on the verge of backing a Federal Bureau of Investigation plan for a sweeping overhaul of surveillance laws that would make it easier to wiretap people who communicate using the Internet rather than by traditional phone services, according to officials familiar with the deliberations.

The F.B.I. director, Robert S. Mueller III, has argued that the bureau’s ability to carry out court-approved eavesdropping on suspects is “going dark” as communications technology evolves, and since 2010 has pushed for a legal mandate requiring companies like Facebook and Google to build into their instant-messaging and other such systems a capacity to comply with wiretap orders. That proposal, however, bogged down amid concerns by other agencies, like the Commerce Department, about quashing Silicon Valley innovation.

While the F.B.I.’s original proposal would have required Internet communications services to each build in a wiretapping capacity, the revised one, which must now be reviewed by the White House, focuses on fining companies that do not comply with wiretap orders. The difference, officials say, means that start-ups with a small number of users would have fewer worries about wiretapping issues unless the companies became popular enough to come to the Justice Department’s attention.

Still, the plan is likely to set off a debate over the future of the Internet if the White House submits it to Congress, according to lawyers for technology companies and advocates of Internet privacy and freedom.