Oxford University has hit back at the prime minister after he said only one black UK student began a course there in 2009 and called it "disgraceful".
The university said David Cameron had been "incorrect and highly misleading", and that at least 26 black British undergraduates started that year.
Mr Cameron was answering questions about the effect of raised tuition fees on poorer students.
Downing Street said the figure of one black Caribbean student was accurate.
Mr Cameron was answering questions from the public at a "PM Direct" event in Harrogate in North Yorkshire.
"I saw figures the other day that showed that only one black person went to Oxford last year," he said. "I think that is disgraceful. We have got to do better than that."
The university said that it was true that only one British undergraduate from that year's intake identified him or herself as "black - Caribbean".
But this failed to take into account another 26 who identified themselves as either "black - African" or "black - other".
Another 14 described themselves as mixed race with some black heritage, a spokesman said.
And these figures do not take into account postgraduates, non-British undergraduates, or undergraduates who preferred not to identify themselves as belonging to a specific ethnic group, he added.
In total, in 2009 22% of Oxford University students were from ethnic minorities, the institution said.
A Downing Street spokesperson said: "The figure the prime minister used was from a response to an Freedom of Information request submitted by David Lammy - which clearly states that only 1 black Caribbean student was admitted to Oxford in 2009.
"The wider point he was making was that it is not acceptable for universities like Oxford to have so few students coming from black and minority ethnic groups."
Mr Cameron was also criticised by the Russell Group of leading universities for saying that the numbers of state-school students had gone down in the last 20 years.
He had said: "That is a terrible record."
But Wendy Piatt, the group's director general, said it was "simply not true", as the proportion of state-school students at Russell Group universities had risen by 9% since 1997.
"This rate of growth exceeds the growth in the proportion of state school students across all UK universities, which was 8.6% in the same period," she said.
Mr Lammy, the shadow higher education minister, said Oxford University "needs to show more humility about its woeful admissions figures".
He said: "It is not acceptable that only one black Caribbean student entered Oxford in 2009. Nor is it clear that Oxford University is really committed to outreach work.
"They targeted private schools for 770 'outreach' events in 2008 and 2009, including 11 at St Paul's and 9 at Eton. This is an issue that is as much about the class and north-south divides as it is about race.
"Oxford is taking more students from Richmond-upon-Thames than they are from Birmingham, Britain's second largest city."
Elite universities are under increasing pressure to boost the numbers of students they attract from disadvantaged backgrounds.
Universities wanting to charge more than the basic £6,000 tuition fees under the new regime, which begins in 2012, must commit to measures to attract poorer students.
Both Oxford and Cambridge failed to increase their share of students from state schools last year, according to data published by the Higher Education Statistics Agency last month.
Both institutions, along with numerous other universities, have said they will charge the maximum tuition fees possible, of £9,000 a year.