The most prestigious UK universities want to charge annual tuition fees of up to £5,000 instead of the £3,000 the government proposes.
Top universities like Birmingham say they need more to compete
The 19-strong Russell Group of research-led institutions said a £5,000 cap would give them more to spend on better facilities for students and recruiting the best academics internationally.
The group's new chairman, Birmingham vice-chancellor, Professor Michael Sterling, said that otherwise the free market ministers wanted would not work.
His comments reflected what the Commons education select committee said recently was the "logic" of the government's position.
The MPs, in their report on the government's strategy for universities, also came up with the figure of £5,000.
RUSSELL GROUP MEMBERS
4 Imperial College
5 Kings College London
8 London School of Economics
15 University College London
Prof Sterling said raising the cap would also enable universities to invest in buildings and equipment.
He said many vice-chancellors were putting off such spending but could not do so indefinitely without losing ground to overseas rivals.
He acknowledged that perception of the debt that students would accumulate was a problem.
But he said they would not have to pay the fees while they were at university - nor will their parents - and graduates earned more money than those without degrees.
"We have got to educate people about the wisdom or otherwise of making an investment and the return you are going to get on that," he said.
Greater income would also allow universities to provide more in the way of scholarships and bursaries for poorer students.
The government plans to let universities charge £3,000 per year from 2006, £1,900 more than now.
Prof Sterling said it would be wrong to imagine that all universities would charge £5,000 for all courses.
"I don't think any would see it as sensible to charge £5,000 across the board, no matter how good they are."
The invitation-only Russell Group - named after the London hotel in which it meets - includes Glasgow and Edinburgh in Scotland and Cardiff in Wales, whereas the government's plans for higher fees apply only to England and, as things stand, Wales.
Lecturers in the new universities responded to Prof Sterling's remarks by accusing the group of "threatening to take their bat and ball home if they can't make the rules".
Roger Kline of the lecturers' union Natfhe said the Russell Group represented a sixth of UK universities - but already received a third of all public money going into higher education and 60% of all research council funding.
"They are establishing an independent lobby to press for their own interests regardless of the impact on the rest of the sector," he said.
Of course all lecturers would welcome the call for better academic salaries, but better pay was needed in all universities - as the select committee and even the prime minister had recognised.
"This is the spectre of the two-tier system which Natfhe and others warned would emerge if variable fees are introduced."
He said it was "disingenuous" to suggest that, once introduced, top-up fees would stop at any ceiling for long.