Plans for universities in England to compete for some student places should be delayed, a Commons committee says.
Under the changes, universities which offer cheaper degrees can bid for extra places, while all will be able to take unlimited numbers of top students.
The Commons Business, Innovation and Skills Committee said the cap on places should not be lifted "overnight".
The government has argued that its plans will mean a better deal for students from poor backgrounds.
In a report on the government's changes to higher education, the cross-party committee said the market mechanisms should only be brought in at least 12 months after tuition fees rise.
Fees in England are due to rise up to a maximum of £9,000 a year from next autumn.
Fees at Welsh universities are also rising to this maximum level, but only for students from other parts of the UK.
In Scotland, Scottish students will continue to pay no tuition fees but those coming from other parts of the UK will pay up to £9,000 a year.
The MPs' report was just about England's plans.
Under these, universities will be able to take as many students as they like if they have scored top grades of two As and a B in their A-levels.
And universities which keep their fees below £7,500 a year will be able to bid for 20,000 places.
In the past, universities were funded for a set number of places.
The report said the delay was needed because consultations on these market mechanisms were still going on.
It said the government had set itself a "challenging timetable" for a "radical overhaul" of the sector and that the changes should be brought in as a package, not in a "piecemeal way".
The committee's chairman Adrian Bailey, a Labour MP, said the "key issue" for universities was the need for a delay in the introduction of the plans to let to universities compete for places.
"If you ask universities what it is they would most like, it is that they would like these changes deferred," he said.
"The crux of the problem is that universities do not know how much money they are going to have next year, because finance follows the student. This is a great cost to them in terms of financial planning."
The committee also called for a re-think on the financial support given to poorer students, saying more money should be given to cover living costs while students were at university rather than in the form of fee waivers (discounts) on fees.
And the MPs called for a "Pupil Premium" such as that being brought in for schools in England, where money follows poorer students.
Universities Minister David Willetts said: "We are putting student choice at the heart of our higher education system. We welcome the committee's acknowledgement of the strengths of the government's reforms, such as better information for students, extension of tuition loans to part-time students, and a clear emphasis on widening participation.
"We have told universities to be much more ambitious with their plans for attracting people from low income backgrounds. University investment in programmes such as summer schools, scholarships and fee waivers will increase significantly.
He added: "We have to get on with ending the present system of setting quotas of places at each university because it lets students down."
Nicola Dandridge, Universities UK's chief executive, said the organisation agreed with the committee's concerns about the speed of the government's reforms.
"The government needs to give universities a period of stability to allow these changes to bed in and to give everyone a chance to understands their implications before any more changes are introduced," she said.
Earlier this week, it was confirmed that 27 universities were lowering their fees from the levels they set earlier in the year, because they had had to do so before the government announced its market mechanisms for places in a White Paper.
Professor Les Ebdon, chairman of the Million+ group, which represents many of the former polytechnic universities, said: "I welcome the fact that MPs have recognised that a great deal of uncertainty has been created for students and universities because of poor communication and too many policy changes introduced by ministers at the last minute.
"MPs are also absolutely right to recommend that changes to student number controls should not be introduced at the same time as changes to the fees and funding system.
"Unfortunately ministers have already jumped the gun and this is exactly what is happening in 2012. This has created further confusion."
In his evidence to the committee, Mr Willetts had addressed criticism about the timetable for the changes.
"I recognise that in a perfect world we might have published the White Paper and then made the specific decision on fees," he said.
"The reality, however, was that the priority for the incoming coalition was to sort out the public finances."
The president of the National Union of Students (NUS), Liam Burns, said: "As students come under sustained financial pressure and struggle to make ends meet, we are pleased that the select committee have recognised the need to prioritise upfront financial support."