Could authoritarian governments gain power over the Web if the U.S. steps out of its role in the Internet domain name system?

That’s been a touchy question for the past four months, since the National Telecommunications and Information Administration announced it wanted to “transition key Internet domain name functions to the global multistakeholder community.”

In other words, the Commerce Department agency wants to get out of the business of administering some functions of the domain name system, a task that it contracted away to a nonprofit international group in 1998. The NTIA has a stewardship and checking role.

Republicans lawmakers have raised concerns about giving up the United States’ formal role, highlighting possible inference by authoritarian governments that want to use their “stakeholder” status to control the Internet beyond their borders.

“Do we think that China, that Russia, that Iran, who  . . .  have a say in the core functions of the Internet have the same concern for the freedom of speech that we Americans do?” asked Wisconsin Republican Sean P. Duffy in offering a House floor amendment last month to slow down the process.

Members have made multiple legislative bids to step into the matter, from backing committee reports that express concern to introducing bills to block the transfer.

For example, the House Energy and Commerce Committee approved a bill by Illinois Republican John Shimkus that would prevent the agency from acting until the Government Accountability Office reports to Congress within a year after any transition plan is proposed. Duffy introduced a bill that would block the agency from moving out of its current role altogether.

Amendments by Duffy and Shimkus were also adopted for the fiscal 2015 Commerce-Justice-Science spending bill and the annual defense policy bill, respectively. And both the committee reports associated with the House and Senate Commerce-Justice-Science spending bills for fiscal 2015 — which would fund the NTIA — say those panels are concerned about the proposal.

For years, the agency has contracted with the private, nonprofit group Internet Corporation for Assigned Names to carry out functions such as those related to implementing updates to what amounts to the Internet’s address book.

The agency’s current contract expires in September 2015, and the NTIA this spring called on ICANN to bring various interests together to come up with a transition plan to create international supervision. ICANN has matured and international support for its type of model keeps growing, the NTIA argues. What won’t be accepted is a proposal that would replace the NTIA’s role with another government or intergovernmental organization such as the United Nations, U.S. officials say.

That doesn’t satisfy some lawmakers. “Once NTIA gives up its current role, who will fill the void?” asked Energy and Commerce Communications and Technology Subcommittee Chairman Greg Walden, R-Ore., at a hearing this spring. “What assurance do Internet users have that such a change will not lead to foreign government mischief?”

It’s very “murky out there” in terms of how this might end, said Sen. John Thune, R-S.D., the top Republican on the Senate Commerce, Science and Transportation panel at a nominations hearing last week.

Shimkus sees that murkiness in the definition of multistakeholder.

“Define for me multistakeholder,” Shimkus said in an interview. Industry and other countries say it’s them, he said.

“So who is it?” he asked.

The looming 2015 date isn’t going to provide enough time for debate, Sen. Marco Rubio, R-Fla., said.

Democrats have argued that NTIA’s announcement is part of a privatization process started long ago, that the endorsement of the multistakeholder model would protect an open Internet and that Republicans are peddling misinformation.

“By creating an artificial delay … the Shimkus amendment suggests governmental meddling in the multistakeholder process is entirely appropriate,” said Rep. Peter Welch, D-Vt., during floor debate.

Authoritarian governments are already using the current U.S. stewardship of technical functions of the Internet as proof that these functions need to move to an entity like the United Nations, he said.

Rep. Anna G. Eshoo, D-Calif., said the House has previously voted in support of the multistakeholder model. “I don’t know where these suspicions have come from that there’s some black helicopter something or other in this,” Eshoo said at a markup of Shimkus’ bill last month.

Matthew Shears, who heads the Center for Democracy and Technology’s Project on Global Internet Policy and Human Rights, says the uncertainty is a legitimate question, but that governmental interference would be anathema to both NTIA and to Internet users and businesses.

That goes back to how the Internet has been fundamentally managed — under a global multistakeholder model, he says.

The Heritage Foundation’s Brett D. Schaefer has said the U.S. government’s role has provided a “bulwark” against political pressure from authoritarian governments that might want to pressure ICANN to, say, block politically objectionable websites.

Of course, no plan has been proposed yet, says Laura DeNardis, an American University professor who focuses on Internet governance. But with the opportunity for two two-year extensions of the planning stage, it is possible that the transition will fall after the Obama administration ends, she adds.

Regardless, DeNardis says concerns about making sure the Internet stays open and free are “valid,” but she’s not concerned about an outsized role for authoritarian governments. And “the administration of the technology has policy implications,” she said.

But what she sees as extreme positions — such as saying “this would be a non-event or that the government is surrendering the Internet” — just cloud the importance of the debate.

“Because,” she says of the mechanics of the shift, “it is a big deal.”