Education watchdog Ofsted wants to toughen the language of inspections in England - changing the "satisfactory" rating to "requires improvement".
Ofsted's chief inspector, Sir Michael Wilshaw, wants to send a message that "satisfactory" is now unsatisfactory and that more schools should be pushing for the higher rating of "good".
This is the latest attempt to improve schools which are seen as "coasting".
The National Union of Teachers criticised such labels as "insulting".
But Prime Minister David Cameron said: "This is not some small bureaucratic change. It marks a massive shift in attitude. I don't want the word 'satisfactory' to exist in our education system. 'Just good enough' is frankly not good enough."
Sir Michael wants to see more schools progressing beyond the current category of "satisfactory", with the change in description intended to emphasise that these schools need to make improvements.
At present, inspectors can judge schools to be "inadequate", "satisfactory", "good" or "outstanding". Subject to consultation, the satisfactory grade will become "requires improvement".
Schools will only be allowed to stay at the "requires improvement" level for three years - and there will be earlier re-inspections, after 12 to 18 months rather than three years, says Ofsted.
Sir Michael was speaking ahead of a Downing Street summit on so-called "coasting" schools - where performance, often in well-off areas, is not necessarily inadequate but has failed to impress.
"There are too many coasting schools not providing an acceptable standard of education," says Sir Michael.
"Of particular concern are the 3,000 schools educating a million children that have been 'satisfactory' two inspections in a row.
"This is not good enough. That is why I am determined to look again at the judgements we award, not only so we are accurately reporting what we see, but so that those schools that most need help are identified and can properly begin the process of improvement.
"I make no apology for making even greater demands of an education system which has to respond with greater urgency to increasingly difficult and competitive economic circumstances."
Prime Minister David Cameron, who hosted the summit, said: "To those who say that this will alienate some schools, I say we've got to stop making excuses and start doing what is best for our children: demanding excellence and confronting complacency wherever we find it."
But teachers' unions criticised the changes - with the NUT claiming that the re-labelled category would be used as a way of pressuring more schools into becoming academies.
"First we had 'underperforming' schools, now we have 'coasting' schools. Labelling schools in this way is derogatory and insulting to pupils, teachers, school leaders and governors," said NUT leader, Christine Blower.
"The government's real agenda behind this change is of course inventing yet another category of schools that it will then seek to force into academy status."
Chris Keates, head of the NASUWT teachers' union, attacked the proposals as "another crude ruse to enable the secretary of state to push more schools into the hands of profit making, private companies".
"The seemingly tough talk we have heard from the government today, may have popular appeal but the reality is that it has nothing to do with raising standards," she said.
"Instead, it is about ratcheting up pressure on schools, without providing the support and resources they need to assist them in securing further improvements.
"This announcement will encourage a culture of vicious management practices within schools which will have a profoundly negative effect on the workforce and children and young people alike."
Labour's shadow education secretary, Stephen Twigg, said coasting schools "need more than just a new label" and criticised the removal of routine inspections of outstanding schools.
"Outstanding schools can quickly slip back, so this measure could undermine confidence in the system and mean parents only get out of date information."
The change to the "satisfactory" category was welcomed by the RSA think tank, which warned about such schools "performing inconsistently".
"What needs to be addressed in particular is the variable quality of teaching. We need to find ways to incentivise the best teachers to join these schools and new ways of helping schools to improve," said the RSA's director of education, Becky Francis.
But head teachers warned that when it came to inconsistency it was Ofsted that needed to get "its own house in order".
"Inspections are too often at the whim of inspectors with little experience in the field they are inspecting and who have already made up their minds before they enter the school," said Russell Hobby, general secretary of the NAHT head teachers' union.
"Heads feel the results can be the luck of the draw. If inspections are getting more severe, then they need to be more consistent and of higher quality or there will be no justice in the findings."