Speaking at the annual conference of the Girls' Schools Association in Stratford-upon-Avon, Mr Patten said that there had been an 'explosion' this year in the number of secondaries that wanted to offer further education.
If these schools could prove that there was a need for sixth-form places in their areas, and that they could provide a high-quality service at a reasonable cost, he would welcome their applications, the Secretary of State said.
Tertiary colleges, which have taken over the education of 16- to 18- year-olds in many areas, could not always provide such in-depth teaching as school sixth forms could, he added.
Mr Patten's announcement came 24 hours after the publication of league tables which showed wide variations in results between schools and colleges. Independent schools and state grammar schools achieved the best A-level results, followed by comprehensive school sixth forms, then sixth-form colleges and further education colleges.
Mr Patten said: ''A school with a thriving sixth form, underpinned by specialist staffing, may be more able to offer attractive subject specialisms to the younger pupils - for example, in technology or modern languages.'
The Secretary of State faced criticism from the girls' schools heads, most of whom are from the independent sector, over the recent league tables, which failed to credit pupils who take exams early, and over plans for a new 'starred' A grade at A-level.
The new grade, aimed at giving recognition to the highest achievers, has found little favour with the independent girls schools which teach some of the country's brightest pupils. Many of them would like to see the A-level abolished.
Sister Jean Sinclair, headmistress of St Leonards-Mayfield in East Sussex, said that the desire to reach an even higher grade at A-level would deflect pupils from other projects, such as learning an extra language or playing an instrument.
After a recent tragedy at the school when a sleepwalking pupil fell from a window and died, she said that sixth-form girls had been able to rally round and comfort the rest of the school.
Sister Sinclair said that the girls had told her: 'In the light of death, what are A-levels?'
Joan Jefferson, president of the association and headmistress of St Swithun's School at Winchester, Hampshire, pleaded with Mr Patten to rethink his commitment to keeping A-levels as 'the jewel in the crown' of the education system.
'We represent some of the most academic schools, not just in this country but in the world. We are not woolly liberals who have gone soft on academic standards, but we think our children need a broader academic background,' she said.
The Government is thinking of using the test results of seven-year-olds to allocate pounds 3.25m for disadvantaged pupils, a document leaked to an MP has revealed.
Stephen Byers, Labour MP for Wallsend, has released a paper presented to an inquiry on the additional educational needs allowance, set up to help children who have medical problems or who come from economically deprived areas. Extra money might be given to areas where test results are low, it says, or to those with high levels of unemployment, poor housing or long-term illness.Reuse content