People considered to be "campaigning" would need to give their real name in their Twitter of Facebook profile page, under plans set out by Conservative chairman Sir Patrick McLoughlin.
And the law would be changed so that those who refused were committing a criminal offence.
At the moment, campaigners can reach thousands of followers on Twitter without making their identities easily available. Examples include the @JeremyCorbyn4PM account, which backs Mr Corbyn and has 141,000 followers but does not provide a name or any other personal details in its profile.
The Tory proposal would mean the people responsible for these and similar accounts - including many thousands of campaigners with much smaller followings - were committing an offence if they failed to add their real names to profile pages for everyone to see.
Sir Patrick set out the plan in a submission on behalf of the Conservative Party to the Committee on Standards in Public Life, which is conducting an inquiry into intimidation of Parliamentary candidates.
The aim is to make it easier to track down people who are abusive on social media, but the measure would apply to everyone.
He said rules which already govern traditional printed literature during an election should be extended to include online campaigning. Under the Political Parties, Elections and Referendums Act 2000, leaflets and posters need to include an “imprint”, giving the name and contact details of the personal responsible, known as the promoter.
This applies to members of the public as well as political parties and other organisations.
Guidance from the Electoral Commission states that the rules cover anything “that can reasonably be regarded as intended to influence voters to vote for or against a political party or a category of candidates”.
Sir Patrick’s proposal is designed to reduce abuse of candidates, following reports that some politicians faced a torrent of hate-filled comments in June’s general election.
In his submission to the inquiry, he said: “To tackle the growth in online anonymous abuse, the Government should exercise Section 143 of the Political Parties, Elections and Referendums Act 2000 to issue regulations to extend imprint rules to electronic material.”
This would require only secondary legislation, avoiding the need for a new Act of Parliament, he said.
Sir Patrick explained: “A Tweet itself (with limited characters) should not have to carry an imprint, but the Twitter account page should.”
He said internet firms would be expected to hand over the personal details of anyone who took part in anonymous online abuse.
But he also made it clear that, under his proposals, anyone who campaigned anonymously would be committing an offence whether they were abusive or not.
He said: “Of course, some third party campaigners could seek to ignore such imprint rules through anonymous content (which would constitute an offence under the proposed extension of imprint rules, over and above the legality of the content)”.
Regulations would set out a definition of "campaigning", to ensure people who issued a single Tweet about politics were not included in the new rules.