The government is planning to fund an additional 60,000 places for first time students in England by 2011.
The annual grant letter to the Higher Education Funding Council for England (Hefce) also urges closer links between universities and industry.
And it wants a continuing effort to widen university participation.
The main academics' union said it was not acceptable to expand student numbers by cutting funding for people returning to higher education.
There has been widespread criticism of the government's plans to withdraw £100m of funding for those doing second degrees or lower qualifications.
The University and College Union said the plans would hit hardest those universities doing the most to widen participation.
The grant letter from the Secretary of State for Innovation, Universities and Skills, John Denham, says public spending on higher education institutions will exceed £7bn this year.
When added to the money for student support, spending would rise by an average of 2.5% each year over the next three years, his department said.
He set out a series of priorities for the sector:
"By 2011, funding for higher education will have increased by over 30% in real terms since 1997, but with increased financial support comes a higher expectation on institutions to widen participation and reach out to new talent by working more closely with schools and employers.
"I believe the opportunities of higher education should be open to all and I am confident that by increasing the number of students in higher education we will deliver a highly skilled workforce and world class research to ensure an economically competitive UK fit for the 21st century."
The chief executive of vice-chancellors' organisation Universities UK, Diana Warwick, said they were pleased to see the extra funding.
"There are still concerns over the funding of part-time education, and we urge the government to ensure that this key area of higher education provision is properly supported."
And they shared the union's concern about students pursuing equivalent or lower qualifications to those they held already.
Sally Hunt of the University and College Union said the funding for a third of the extra 60,000 student places was money being taken away from those doing second degrees and other courses.
"We do not believe that slamming the door on thousands of people who want to retrain or refresh their skills is the best approach," she said.
"Our major concern is the stated aim of the Department for Innovation, Universities and Skills to make 'efficiency savings' rising to £1.5bn a year by 2010-11.
"We want the department to fully consult with the higher education sector before any cuts in funding are announced."
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