Cyber-bullying, trolling and under-age access to porn will be targeted in plans drawn up by Karen Bradley to make the online world safer.
Social media companies will be hit by an industry-wide levy to fund measures to deal with online harm.
A new code of practice to tackle bullying, intimidating or humiliating online content would be also be created.
The Culture Secretary defended making the levy voluntary despite the Tory general election manifesto promising legal powers to enforce such a move.
She told BBC Radio Four’s Today programme: “I don’t rule out legislating if that’s what we need to do but I hope we can do it on a voluntary basis working with the companies.
“It’s not backing away at all. It’s saying: ‘What is the best way to do this?’”
Mrs Bradley said the Government was looking at whether social media companies should be classed as publishers rather than platforms.
Such a move could mean greater regulation of social media content.
The Culture Secretary said: “We are looking at their role and their responsibilities. And we are looking at what their status should be. They are not legally publishers at this stage, but we are looking at this issue.
“That’s what we are looking at, as to how we can make sure that we do regulate the internet in an appropriate way.”
Mrs Bradley said the opportunities of the internet need to be embraced, adding: “But we have to do it in a safe way, and we have to it in a way that respects content as much as anything else and that’s one of the issues about the status of internet companies and social media companies.”
The proposals outlined in the Internet Safety Green Paper also include an annual internet safety transparency report to keep tabs on online abuse.
Support would be given to digital start-ups to make sure they build safety features into new apps.
The Government also confirmed plans announced earlier this year to make relationship lessons, which will include online safety, compulsory in schools.
It highlighted research from the UK Safer Internet Centre that found 64% of 13-to-17-year-olds have seen people posting offensive images or videos.
Opposition parties called for more detail and stronger policy.
Shadow culture secretary and Labour deputy leader Tom Watson said: “We’re pleased the Government has accepted Labour’s call for compulsory sex and relationship education in schools, including online safety education, as well as for codes of practice for social media companies to prevent abuse.
“But this announcement is short on detail. The Government needs to say more about who exactly will pay the proposed levy, how much they will pay and how it will be spent.
“They need to explain what transparency information they will be asking social media companies to provide.”
Liberal Democrat home affairs spokesman Sir Ed Davey said: “The substance in this Green Paper falls far short of its ambitious title.
“We must make the internet a much safer place - particularly for young people.
“That means the hard graft of better digital education, faster reporting of problems and stronger partnerships with industry.
“Regrettably, this Government is still in the blame game, scapegoating and castigating internet firms, and failing to see the huge economic benefits of investing in better digital education.
“Hopefully this Green Paper will be the last of the weak policy reheats and signal the start of real hard work on this issue.”
Facebook said it welcomed “close collaboration between industry, experts and government to address this important issue”.