Gavin Williamson also told MPs he believes pupils “would not be facing” bubble arrangements in September.
Labour warned data showed 375,000 children were out of school last week as a result of Covid.
Answering an urgent question on the impact of Covid on young people’s attendance in education, Mr Williamson told the Commons: “What I want to see is these restrictions including bubbles removed as quickly as possible along with wider restrictions in society.
“I do not think it is acceptable that children should face greater restrictions over and above those of wider society especially since they have given up so much to keep older generations safe over the last 18 months."
It comes as concerns have been raised in recent weeks and months about the interpretation of rules which have resulted in large groups of pupils being sent home for 10 days if another pupil in their bubble tests positive for Covid.
Williamson added: “Further steps will be taken to reduce the number of children who have to self-isolate including looking at the outcomes of a daily contact testing trial as we consider a new model for keeping children in schools and colleges.
“We constantly assess all available data and we expect to be able to confirm plans to lift restrictions and bubbles as part of Step 4.
“Once that decision has been made we will issue guidance immediately to schools.”
Step 4 of the road map is expected to take place on July 19.
He added he wants to end regular Covid testing for schoolchildren “at the earliest and most realistic possible stage”, although he acknowledged this was a long-term aim, amid calls for schools to “move back to normal”.
Mr Williamson went on: “As we open wider society up, we will stick to the principle that children’s education and freedom comes first.”
He added: “I’m looking carefully every day at how we manage the balance between safeguarding children’s education and reducing the transmission of the virus, because I know that there is still too many children having their education disrupted, no matter how good remote education is that they are receiving.
“The new Health Secretary (Sajid Javid) and I have already discussed these matters and I’m working with him across my department as well as with scientists and public health experts to take the next steps.”
For Labour, shadow education secretary Kate Green said: “School leaders dread another last-minute announcement, they need time to put plans in place and their staff also desperately need a break over the summer.”
Additional reporting by PA.