The Conservatives say they want to give people the power to demand social media companies delete any embarrassing content they posted as children.
The party has promised to introduce “new protections against internet harms” if they win the election.
It wants to work with social media firms such as Facebook and Twitter but have not ruled out legislation.
Labour accused the Tories of “cynically trotting out tough talk that we know will be ultimately meaningless”.
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.
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.
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” in a Guardian interview
- 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 by at least 2.5% every year
Election campaign latest
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.
Companies would also be required not to direct users “unintentionally” to hate speech and other sources of harm.
The Tories said the new digital entitlements and protections “will be backed up with a statutory sanctions regime” which would give regulators the ability to fine or prosecute those companies who failed in their legal duties, and to order the removal of content where it clearly breached UK law.
But Labour’s digital economy spokesman Louise Haigh said: “We pressed the government to introduce tough new codes to tackle extremist and illegal content proliferating across the web, but they categorically refused to act in the Digital Economy Act.
“The Home Office were crystal clear they did not want to legislate and that they believed the voluntary framework was sufficient.
“Now only three weeks on from those discussions, they’re cynically trotting out tough talk that we know will be ultimately meaningless.
“The fact is that in government the Tories have been too afraid to stand up to the social media giants and keep the public safe from illegal and extremist content.”
Analysis: By BBC Political Correspondent Chris Mason
The Conservatives want to be seen to be alive to the realities of the digital age for young people.
Photos vividly illustrating teenage indiscretion, or controversial commentary posted online which may prove rather tricky to defend years later in a job interview, can be very difficult to get rid of, without the user deleting their entire profile.
Attempting to regulate global social media companies, based outside the UK, isn’t easy.
But the Conservatives are promising a new law under which these internet giants would be fined if they ignored the wishes of a user who had turned 18 and wanted material removed from when they were younger.