"We haven't found anyone who is against it yet, so that's a good sign," Rubio told reporters after the committee vote.
Proposals to give the U.N.'s International Telecommunication Union (ITU) more control over the governance of the Internet could come up at a conference in Dubai in December.
The proposals, reportedly backed by China, Russia and other U.N. members, would give the international body more control over cybersecurity, data privacy, technical standards and the Web’s address system.
The Obama administration has already announced its strong opposition to such proposals.
The Internet is currently governed under a “multi-stakeholder” approach that gives power to a host of nonprofits rather than governments.
The resolution would urge the administration to "promote a global Internet free from government control and preserve and advance the successful multi-stakeholder model that governs the Internet today."
"I just want to be clear that America is on record as being in favor of Internet freedom and that we don't want to see any internationally recognized right for government interference on the Internet and the free flow of information on the Internet," Rubio said.
Sen. Claire McCaskillClaire Conner McCaskillRepublicans may regret restricting reproductive rights Sunday shows preview: States deal with fallout of Ida; Texas abortion law takes effect Giuliani to stump for Greitens in Missouri MORE (D-Mo.) is a lead co-sponsor of the legislation.
“I’ll continue to fight to ensure our bipartisan bill gets a vote on the Senate floor and that we continue to work across the aisle to encourage business growth and development, and that we’re not giving oppressive regimes more tools to silence democratic dissent by their people,” McCaskill said in a statement.
The National Cable & Telecommunications Association applauded the vote, saying it sends a "strong message that the flow of information free from government control is vital to democracy, commerce, education and much more across the globe."
The Software & Information Industry Association also praised the senators for bringing attention to the issue.
“We must put the full weight of the United States behind efforts to maintain a global Internet free from unnecessary international governmental control," the group said in a statement.
—Updated at 5:01 p.m.