Controversial measures which would have forced big technology platforms to take down legal but harmful material have been axed from the Online Safety Bill.
Critics of the section in the bill claimed it posed a risk to free speech.
Culture Secretary Michelle Donelan denied weakening laws protecting social media users and said adults would have more control over what they saw online.
The bill – which aims to police the internet – is intended to become law in the UK before next summer.
But some have criticised the latest changes, including Labour and the Samaritans who called it a hugely backward step.
Ian Russell, the father of teenager Molly Russell who ended her life after viewing suicide and self-harm content online, said the bill had been watered down and the decision may have been made for political reasons to help it pass more quickly.
The bill previously included a section which required “the largest, highest-risk platforms” to tackle some legal but harmful material accessed by adults.
It meant that the likes of Facebook, Instagram and YouTube, would have been tasked with preventing people being exposed to content like, for example, self-harm, eating disorder and misogynistic posts.
Instead, tech giants will be told to introduce a system allowing users more control to filter out harmful content they do not want to see.
Ms Donelan told the BBC the bill was not being watered down – and that tech companies had the expertise to protect people online.
“These are massive, massive corporations that have the money, the knowhow and the tech to be able to adhere to this,” she said.
She warned that those who did not comply would face significant fines and “huge reputational damage”.
Some critics of the provision in the bill have argued it opened the door for technology companies to censor legal speech.
It was “legislating for hurt feelings”, former Conservative leadership candidate Kemi Badenoch said.
And in July, nine senior Conservatives, including former ministers Lord Frost, David Davis and Steve Baker, who has since returned to the government, wrote a letter to then Culture Secretary Nadine Dorries, saying the provision could be used to clamp down on free speech by a future Labour government.
Adults will be able to access and post anything legal, provided a platform’s terms of service allow it – although, children must still be protected from viewing harmful material.
Mr Davis told the BBC he was glad that the legal but harmful duties had been taken out the bill but he still had other “serious worries” about the threat to privacy and freedom of expression which could “undermine end-to-end encryption”.
Lucy Powell MP, Labour’s shadow culture secretary, criticised the decision to remove obligations over “legal but harmful” material.
She said it gave a “free pass to abusers and takes the public for a ride” that it was “a major weakening, not strengthening, of the bill”.
And the boss of charity the Samaritans, Julie Bentley, said “the damaging impact that this type of content has doesn’t end on your 18th birthday”.
“Increasing the controls that people have is no replacement for holding sites to account through the law and this feels very much like the Government snatching defeat from the jaws of victory.”
But Ms Donelan told BBC News the revised bill offered “a triple shield of protection – so it’s certainly not weaker in any sense”.
This requires platforms to:
remove illegal content
remove material that violates their terms and conditions
give users controls to help them avoid seeing certain types of content to be specified by the bill
This could include content promoting eating disorders or inciting hate on the basis of race, ethnicity, sexual orientation or gender reassignment- although, there will be exemptions to allow legitimate debate.
But the first two parts of the triple shield were already included in the draft bill.