The findings follow figures this week showing that the number of teachers suffering serious injuries doubled last year, leading to calls for tougher action against "classroom yobs" (see page 2).
Many students questioned by the agency - including some trained in Wales - said their courses also failed to help them teach children from ethnic-minority backgrounds.
Researchers, who surveyed a third of the 31,800 trainees gaining teaching accreditation in 2004, found general satisfaction with the standard of courses. In total, 84 per cent rated university or school-based courses as good, some of the best feedback received since the survey was launched six years ago.
But behaviour in the classroom remains one of the key concerns. Only 65 per cent said courses helped them to maintain a good standard of behaviour, with the remainder rating training as merely adequate or poor. Students trained directly in the classroom found they could cope better than those on university-based courses.
The agency said the findings showed a significant year-on-year improvement but that there was much room for improvement.
The admission follows the creation of a new behaviour taskforce by the Department for Education and Skills to co-ordinate a fresh campaign against violent pupils in England.
The agency's researchers found that only a third (35 per cent) of trainees said they were well prepared to teach pupils from minority backgrounds and 27 per cent were confident in front of children who spoke English as a second language.
Dominique De-Iuliis, 23, a design and technology teacher at John Cabot city technology college, Bristol, who trained at the University of Wales Newport, said: "I was pleased with my training - it prepared me for what it would be like teaching. There wasn't a specific section on teaching ethnic-minority pupils, but we were taught general strategies that have helped and personally I've never found it a problem."
The survey also showed that just over half of teachers felt prepared for their induction year and 77 per cent said they had a good understanding of the national curriculum, down slightly on 2003.
The findings follow a study last week which revealed increasing numbers of trainee teachers are experiencing problems securing their first job.
An analysis of Teacher Training Agency figures by Buckingham university revealed that a third of primary trainees who qualified last summer had not found work six months after completing courses.
Primary trainees in south Wales have again been finding it extremely difficult to get jobs this summer.
But there is also an acute dearth of primary jobs in the north of England.
One university told The TES this week that only 103 out of 318 newly-trained teachers had so far succeeded in finding work for September.