Most people in England think teachers' pay should be linked to their classroom performance, a survey suggests.
Of 1,723 people polled by Populus, 62% said schools should be able to set salaries in line with performance.
Education Secretary Michael Gove said this showed the public wanted teachers' pay linked to quality of work.
But unions say the changes are really about cutting most teachers' salaries and that most parents want schools to follow a national pay system.
Of those surveyed, 43% said the most important factor in deciding teachers' pay should be the quality of their teaching, determined by an annual appraisal, while 29% said it should be the quality of their teaching determined by their pupils' exam results.
Smaller proportions said that pay should be based on length of service, the number of professional qualifications a teacher had or to ensure parity with other teachers in the school.
Just over one in four (28%) agreed with the statement: "Two teachers doing the same job in the same school, for the same length of time, should always receive the same salary packet, regardless of the outcome of their annual performance appraisal."
The survey also asked about two teaching unions' planned strike action, in protest at government changes which will see teachers' pay linked from September to their performance.
The National Union of Teachers (NUT) and the NASUWT have announced regional strikes in October, followed by a one-day national walkout later in the term, in a row over pay, pensions and working conditions. It follows a strike in the north-west of England in June.
In the NUT's ballot in September, 82.5% voted in favour of strike action with a turnout of 27% while 82% of NASUWT members voted for industrial action, with a turnout of 40%.
The Populus poll found 29% of those asked supported the unions' plans for industrial action, while 36% were against it.
A further 34% said teachers should be banned from striking because they provided an essential public service, like the police.
Populus strategy director Rick Nye said: "These findings show strong public support for a move away from the automatic annual pay rises of the past towards performance-related pay in schools."
Speaking at a Populus event in central London, Education Secretary Michael Gove said the NUT and the NASUWT were standing in the way of the profession "enjoying the prestige that it deserves".
Mr Gove said the justification given by the unions for taking industrial action didn't "wash with the public" and urged them to call the strike off.
"I think the public are absolutely right. I think it is hugely irresponsible for the teaching unions to go on strike at this point.
"The basis for which they are going on strike is beyond me. It seems to be an amalgam of moans and groans and objections to government policy which don't amount to an appropriate mandate for industrial action and so they don't pass muster with the public.
He said the strike decision did not show teachers as "harbingers of greater prestige for the teaching profession, but as defensive, left-wing, ideologically committed to keeping teachers imprisoned in a model of labour relations that was already out of date in the 1970s".
NUT general secretary Christine Blower said a recent poll by her union had found 25% of parents thought schools should set their own pay system, while 60% backed a national pay system.
"The government's proposals are about cutting the salary of the majority of teachers, not rewarding them for the work they do," she said.
"There are already provisions for withholding salary progression where teachers are underperforming and the consistent attack by this government on the high quality of teaching that is delivered by the overwhelming majority of teachers every day in schools is a disgrace."
Ms Blower added: "Teachers have been left with no option other than to take industrial action in the face of the continuing onslaught on their pay, pensions and working conditions and the refusal of this government to enter into any meaningful negotiations."
Dr Mary Bousted, general secretary of the Association of Teachers and Lecturers, accused Mr Gove of trying to make "political capital out of a sub-standard poll with incredibly leading questions".
"There is no evidence that performance-related pay for teachers will improve education for children, which should be the government's over-riding priority.
"Nor is there any evidence that performance pay will motivate teachers, or attract or retain the best teachers, all of which have a significant impact on children's education."