The Conservatives say they want to give people the power to demand social media companies delete any embarrassing content they posted as children.
The largest firms would be required, if requested, to erase material created by someone before they turned 18.
Ministers hope for co-operation from the likes of Facebook and Twitter but may impose fines if they do not comply.
Labour said despite the "tough talk" ministers had proved unwilling to "stand up" to the industry in the past.
But Home Secretary Amber Rudd told BBC 5 live the party had had "early conversations" with social media companies which indicated they were willing to work with the government on introducing "new protections against internet harms" if the Conservatives win the election.
At present, users can delete their profile on social media accounts if they want to get rid of embarrassing content, but this risks losing all their online connections with people.
Ms Rudd said further safeguards were needed to ensure that "inappropriate" content from yesteryear did not become a hindrance for people when they starting applying and being interviewed for jobs.
In other election news:
Labour's deputy leader Tom Watson has urged people to vote for his party to avoid a "Margaret Thatcher-style landslide"
Lib Dem leader Tim Farron has pledged to ensure 300,000 homes are built each year and give councils the power to hike tax on empty properties
Labour has repeated its pledge to enshrine in law the "triple lock" commitment to raise pensions in line with wages, inflation or by 2.5% - whichever is highest - every year
The right to remove, which would be introduced via legislation, would apply to users of "major" social media platforms and cover all of their own records before adulthood.
Tory sources said the plan was not "overly prescriptive" and indicated that the question of content being tagged and shared by other people would have to be addressed.
The Conservatives also want to make it easier to conduct business online, by introducing the right to insist on a so-called digital signature as a replacement for signing a contract by hand.
The Conservatives want the social media industry to find technological changes that will protect minors from images of pornography, violence and other age-inappropriate content on social media, app stores and websites.