Schools standards minister Estelle Morris issued the challenge as the agency, whose remit was scaled down by the Government six weeks ago, unveiled a blueprint for its future.
At the launch of the agency's new three-year corporate plan, Ms Morris said: "There is nothing more important than recruiting good people to the profession. The challenge is to persuade more of those who have very good grades from the sixth form, and university graduates with very good degrees, to become teachers."
Ms Morris told the audience at the Gibson Hall, in the City, that a key to this was the Green Paper on modernising the profession, which would create a more structured and attractive career for recruits.
"I have always felt that part of the problem in recruiting people to teaching was the product we were selling. What was needed was something that said to the most able, ambitious youngster: you will be allowed to progress quickly, if you are up to it, and if you perform well you will be rewarded."
The new corporate plan includes sections on promoting teaching and raising the standards of initial training. It sets targets of increasing the proportion of ethnic minority recruits from 6 per cent now to 9 per cent, in line with the school population, and raising the numbers of men and people with disabilities entering the profession.