Academies, free schools and others outside of local authority control will not be affected.
Free schools are a flagship part of the government's reforms to education in England.
Mr Gove also used the committee session to defend his policies for academies and free schools.
Time is running out for applications to run two new free schools in Berkshire.
But the government said most free schools were in areas with the "greatest pressure on places".
The DfE said it had no plans to reassess its list of approved free schools.
BBC: LGA head: 'Government should reassess new free schools'
Government free schools are semi-independent and are set up by groups including parents and charities.
Currently academies and free schools are expected to comply with the standards on a voluntary basis.
Free schools are semi-independent state schools set up and run by parents, teachers and charities.
Academies and free schools in England are not bound by government regulations on school food.
Critics have called free schools, which are state-funded but privately run, socially divisive and unaccountable.
Ian Goodyer, of Suffolk Coalition Opposing Free Schools, said the school was still "woefully undersubscribed".
Ensuring effective intervention when things go wrong in academies or free schools is another.
Yet the council helped choose the free schools' locations by finding empty premises to accommodate them.
That means creating more free schools and academies so that there is a better educated workforce.
Succeeding without selecting will also be the challenge for Mr Gove's other supply-side initiative: free schools.
ECONOMIST: State schools and selection: The religious and the rational | The
And he said the findings did not provide evidence for the current government's support for free schools.
The vast majority of open mainstream free schools are in areas with the greatest pressure on places.
BBC: LGA head: 'Government should reassess new free schools'
The government says it wants the total number of free schools to "at least double" next year.
The principle is simple: All parents should be free to choose good, safe, drug-free schools that work.
"We don't think there's any pent up sense of huge parental demand for free schools, " he said.
Free schools are state-funded schools which are set up by groups of parents, charities or other providers.
By the end of this year half of all British schools will be academies or free schools.
"The majority of open mainstream free schools are in areas with the greatest pressure on places, " he said.
Mr Courtney said free schools were being opened when primary schools were having to add on temporary classrooms.
Most recently, the foundation introduced the Plastic Free Schools program to reduce single-use plastic on the Hawaiian Islands.
Mr Miliband also rejected calls to back a return to local authority control for free schools and academies.
There are about 80 free schools open in England now, with another 100 planned to open in September.
The coalition is also pushing free schools, created by parents and other groups dissatisfied with the local offerings.
Free schools are being opened in parts of England where there are surpluses of places, a teachers' union says.
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