Current targets will become too narrow a measure of success as schools move towards more personalised learning, the education secretary has said.
Alan Johnson said targets had produced "massive improvements"
Alan Johnson also suggested a shake-up of the system could encourage some schools to seek out bright pupils from disadvantaged backgrounds.
He said reform plans for England would be announced soon.
The National Union of Teachers has welcomed his comments and called for the scrapping of league tables.
Mr Johnson told a meeting of new head teachers in London, organised by the National College of School Leadership, that school targets had produced "massive improvements" and were "here to stay".
But he added: "They do not tell the whole story."
They conceal "tales of amazing achievement on the one hand and substantial groups of disadvantaged kids left behind on the other", he said.
"Threshold targets focus everything on a narrow time and performance window, failing to take account of potential or progress over a longer period."
Thresholds are, for example, the proportion of pupils attaining a certain level or number of qualifications - such as five good GCSEs.
Mr Johnson said it was not a success if a child who was expected to obtain eight A grade GCSEs only achieved five moderate grades.
But if a pupil who was expected to achieve nothing got their English and maths GCSEs then it was an achievement worth recognising, he added.
He said he had a "genuinely open mind" about how measures of a child's progression could "supplement" the existing targets system.
"Should we look at schools in terms of the overall numbers of pupils making progress at each stage?
"Should we move over time to a system where all pupils are expected to progress by at least two levels, say, in each key stage in reading, writing and maths? How long might that take?"
The education secretary said £1bn was being spent to bring about pupil-centred personalised learning in England's schools - equivalent to about £135 per pupil.
Mr Johnson said the funds would "maximise the chances of every pupil to progress".
So-called "value added" progress measures are already published.
From this year, the school performance tables will also reflect such "contextual" factors as pupils' ethnicity, gender, social deprivation and special educational needs.
But the targets schools have do not relate to these.
The general secretary of the National Union of Teachers, Steve Sinnott, said personalised education was in direct contradiction to crude national targets.
"But he needs to go further. League tables are not inevitable. Other countries have shown they can do without them. They should go."
The head of the Association of School and College Leaders, John Dunford, said consideration of new progress measures was long overdue.
The threshold GCSE measure "skews policy and forces schools to allocate scarce resources to particular areas", he said.
"A measure based on the progress that each individual student makes from one key stage to the next represents a step towards a more intelligent accountability system, as ASCL has long advocated."
Shadow education secretary David Willetts said Mr Johnson was at last admitting that some children from poor areas were getting a raw deal from their education.
"But Alan Johnson failed to address the crucial point. It is tried and tested teaching methods that benefit children of all abilities."
Liberal Democrat spokeswoman Sarah Teather said struggling pupils were too often left behind under the rpesent "regime".
"Funding shouldn't be focused on geographical areas or classes of people, but directly on those children who are under-achieving," she said.
"This 'pupil premium' would create the necessary incentive for schools to take on challenging pupils."