Providers which fail to meet new targets for recruiting more ethnic-minority students could also see the number of places they can provide slashed, leading to cuts in funding.
"They simply have to increase their numbers, unless there is a very good reason why not," said the agency's chief executive Anthea Millett, speaking at a London conference last week. "Naming and shaming is certainly a serious option."
Ms Millett's comments are designed as a warning shot to those providers seen to be dragging their heels. Last year the agency instructed all providers to set targets increasing their numbers of ethnic-minority students year-on-year.
More than two thirds have already set new targets, but Ms Millet said at least two institutions were still refusing to do so. "That is just not acceptable," she said.
At present only 6 per cent of entrants to teaching are from an ethnic minority, reflecting the overall national population. However, the agency wants that figure to increase to at least 9 per cent, more accurately reflecting the ethnic breakdown of school pupils.
Providers with a high number of black and Asian students, such as the University of North London, will be rewarded with extra places and more money.
Ms Millett also criticised ethnic-minority groups for failing to consider teaching in the first place. She said: "There is often a substantial amount of resistance to teaching as a career. There is a job to be done on both sides."
However, a new report from the Strathclyde University, to be published in August, says that experiences of racism at school discourage many black and Asian people from contemplating teaching.
Dr Russell Jones at Liverpool John Moores University, who has recently surveyed trainee teachers for their views on race, said the agency was "concerned only with its own recruitment figures without bothering to acknowledge why black and Asian teachers find the profession so deeply unattractive."
The agency moves follow fierce criticism that until now it has been "colour-blind" on race issues.