WASHINGTON—Big internet firms on Tuesday told federal regulators that they would oppose Republicans’ plans to roll back net Obama-era neutrality rules, adding to signs of a looming political clash.

The Internet Association, a trade group that includes companies such as of Netflix Inc. and Facebook Inc., told Federal Communications Commission Chairman Ajit Pai in a meeting that it “continues its vigorous support of the FCC’s [net-neutrality] order,” the group said in a regulatory filing. It added that the net-neutrality rules...