The government is committed to implementing social media restrictions for under-16s but ministers must "make sure it works" before introducing changes, the Education Secretary Bridget Phillipson has told the BBC.
The government is consulting on an outright ban, as well as other measures designed to stop teenagers accessing addictive and harmful material.
Phillipson's comments came after junior education minister Olivia Bailey said the government would "impose some form of age or functionality restrictions" even if it stopped short of a ban.
Campaigners have called for an Australia-style ban on children using social media, but there are questions about how effective the prohibition has been.
Monday saw the latest stand-off between the government and House of Lords over the Children's Wellbeing and Schools Bill, which would give ministers the power to introduce sweeping restrictions on social media usage.
Peers have repeatedly pushed the government to press ahead with a ban, voting in favour of opposition amendments on four occasions.
The government proposed further amendments to the bill on Monday in an effort to end the deadlock, including one which would give ministers the power to implement a ban in the future but stops short of introducing as quickly as the Lords had called for.
MPs supported the government's changes to the draft law by 272 votes to 64, with the bill now returning to the Lords for what looks to be the final consideration before it receives royal assent and becomes law.
On Monday, Bailey said the government was making a legal commitment that it "must" act once its consultation restrictions concludes on 26 May, but did not give specific details about the action ministers would take.
She told the Commons: "Let us be clear: the status quo cannot continue. We are consulting on the mechanism and that is the right thing to do.
"But we are clear that under any outcome we will impose some form of age or functionality restrictions for children under 16.
"I can also confirm that consideration of restrictions such as curfews will be in addition not instead of this."
Bailey said the government is "focused on addictive features, harmful algorithmically-driven content and features".
It remains unclear what specific restrictions the government may implement, short of a under-16s social media ban.
But in asking whether children should have unrestricted access to AI chatbots or if age verification rules should be strengthened, its consultation may provide some clues.
There has also been increased scrutiny over mechanisms used by social media sites to keep people engaged – such as letting users endlessly scroll through and refresh content.
Such design features were recently highlighted in a landmark US social media addiction trial, which saw Instagram-owner Meta and YouTube found liable for building addictive platforms that harmed a young woman's mental health.
Social platforms operating in the UK are already required to show their efforts to make children's experiences safer.
Under the Online Safety Act, they must assess whether and how safety risks to children appear on their sites, including through features such as content recommendations or predictive search functions, and mitigate these.
They must also enforce their age requirements, such as with age-appropriate experiences for children and teenagers.
Some social media giants like Meta have rushed to implement these, among many other controls, to comply with the rules and similar regulations worldwide – and stave off a potential under-16s ban.
But many campaigners argue existing rules and actions have fallen short of delivering protections children need to have safer, healthier experiences online.
Bailey said a "progress report" must be made three months after the Children's Wellbeing and Schools Bill receives royal assent, adding this reflects "our intention to quickly produce a response following the consultation".
She added: "Following this we will have 12 months to lay regulations, but our firm intention is to move faster and [Technology Secretary Liz Kendall] has been clear that we aim to do this before the end of the year."
Bailey said the government would, in "exceptional circumstances", have the option to extend the timeline by a further six months but they would have to explain to Parliament why this is needed.
Speaking to BBC Breakfast on Tuesday, Phillipson said there were a range of views on what measures to impose among campaigners and the consultation would determine "the shape of that action".
After Monday's vote, shadow education secretary Laura Trott said there was now a "commitment on the floor of the House from the government that they will impose an age restriction for children under-16".
She added: "This is a huge step forward in keeping children safe and supporting parents in their fight against screens destroying children's lives."
Liberal Democrat leader Sir Ed Davey accused the government of "ducking" the issue during Monday's votes, telling BBC Breakfast: "I think this is just an excuse for the government not to take action. They could have set a timetable in law to force their hand. They need to have moved faster."
He added: "If you look at the mental health impact on children, the devastation its caused for some families, I'm afraid kicking the can is not an answer, we need action and we need it in the next 12 months."
Conservative former schools minister and academy chain founder Lord Nash, who led calls for a social media ban in the House of Lords, thanked the government for saying it would act.
He said: "We will now all turn our attention - together - to making sure this is implemented as soon as possible in the best way to protect our children."
Lord Nash also thanked bereaved parents for their support in the campaign.
Ellen Roome, from Cheltenham, who believes her son Jools Sweeney, 14, died while trying a dangerous online challenge, told BBC Breakfast she was "so pleased" the government had committed to taking action.
"There parents who are absolutely delighted, there was a lot of tears last night," the campaigner said.
"We've just done as much as we can to say 'please make a difference for everybody else's children as its too late for us'."
Andy Burrows, chief executive of the Molly Rose Foundation, which campaigns for online safety meadures, welcomed the decision but said it must "go beyond a blanket ban" which offered limited action and a false sense of safety to parents.
"It's crucial that tech companies are forced to act to make their products safe off the back of the consultation," he said.
Additional reporting by Liv McMahon
