The FCC had received about 780,000 comments as of Tuesday afternoon, with about 222,000 coming through its electronic comment system, said spokeswoman Kim Hart.
The pace of filing accelerated as the deadline of midnight EDT Tuesday approached, and many people have been unable to access the site, she said.
"Not surprisingly, we have seen an overwhelming surge in traffic on our website that is making it difficult for many people to file comments through our electronic comment filing system," Hart said. "Accordingly, we are extending the comment deadline until midnight, Friday, July 18."
The FCC's proposed rules governing Internet traffic have triggered protests outside the agency's headquarters and intense interest among Internet companies, broadband providers and the public.
Consumer groups and online activists have complained the rules are too weak to prevent broadband service providers from interfering with content flowing through their networks and have encouraged Americans to contact the FCC to urge tougher regulation to ensure net neutrality.
The surge in comments followed a viral rant by HBO's John Oliver urging the public to contact the FCC and push for strong net-neutrality rules.
Expecting an outpouring of comments, the FCC set up an alternative system in April that allows people to submit their views via email to firstname.lastname@example.org.
As of Tuesday, the FCC had received about 558,000 email comments, Hart said.
The agency's information technology team on June 3 also added additional capacity to the online comment system, David A. Bray, the FCC's chief information officer, said in a blog post Monday.
"The number of people submitting comments is impressive, underscoring the importance of this issue and the critical role public engagement plays in the commission’s policy-making process," Bray said.
After Friday's extended deadline, the public will have until Sept. 10 to reply to comments made during the first round of public input.