Ministers want 50% of young people to go to university
Universities Secretary John Denham insists the Westminster government is not going to "start meddling" in the way universities choose students.
He said the target to have half of all young people in higher education was right but ministers were not forcing universities to take poor students.
The head of Cambridge University has warned that the importance of universities "encourages meddling".
But Prof Alison Richard said their core mission was not social change.
Speaking on the Today programme on BBC Radio Four, Mr Denham said fair access to universities was vital.
"We can't afford to waste the talents of young people in this country and widening participation to higher education in general, and fair access to the most competitive selective universities, is crucial.
"We work with universities in many ways to make the case for widening participation and also to encourage universities to work with schools as they do to get students to apply to universities," he said.
"What we don't do is tell individual universities how to run their admissions policies. Our universities' strength depends on their autonomy and there is a line we don't cross.
"So we will argue passionately that we are not making the best use of too many people who are very able, we want to see change in schools and universities but we are not going to start meddling, interfering in how they run their admissions procedures."
The National Audit Office reported earlier this year that although people from lower socio-economic backgrounds make up around one half of the population of England, they represent just 29% of young, full-time entrants to higher education.
However, it also said participation in higher education by people from low income groups had increased more than that of better off groups in the past 10 years.
'Tempest in a tea cup'
Universities are given targets, or "benchmarks" as they are termed, for the proportion of students they should be taking from low income or "non-traditional" backgrounds.
This target is not linked to funding.
However, separately, universities receive extra money for the number of students they take from areas where not many young people go to university.
England's higher education funding body, Hefce, says this is designed to cover the costs of recruiting such students - by doing outreach work in schools, for example - and of supporting them in their first year because they are more likely to drop out.
To be allowed to charge top-up tuition fees, universities also have to set out their arrangements for bursaries for low income students in what is known as an "access agreement" with the Office for Fair Access (Offa).
The president of Universities UK and head of Kings College London, Rick Trainor, said the controversy sparked by Alison Richard was a "tempest in a teacup".
He said the comments had been made in a speech which was generally positive about the UK university system and relations between universities and the government.
"There is a real commonality of purpose between universities and government about trying to get the best students into our universities, of whatever kind - the people who can most profit from a university education," he said.
In a speech to university leaders at University UK's annual conference, Mr Denham said: "It has been suggested that universities, and by extension, education, is not an engine for social justice. I have to say I profoundly disagree.
"Education is the most powerful tool we have in achieving social justice. From that recognition, the responsibility arises not to lower standards but to seek out, support and nurture talent, wherever it exists."
In an interview with the Times, Prof Richard had said a university's core mission was not to promote social mobility, but to "provide an outstanding education within a research setting".