Ms Kelly set out the plans in a speech to the annual conference of the National Association of Schoolmasters Union of Women Teachers (NASUWT) in Birmingham.
Schools seen as under-performing will be sent warning notices by local authorities and will be given 15 days in which to respond.
If a council is unhappy with the rescue plan, the school will have 24 hours before a team is sent in.
A DfeS spokesperson told LGCnet that the 15 day period 'relates to the time they have to reply to a warning notice and show that they have an appropriate improvement strategy'.
Ms Kelly's speech was accompanied by draft guidance from the DfeS on the powers, which relate to Part 4 of the Education and Inspection Bill.
As well as setting out revised laws on early warnings, the guidance stresses that local authorities 'must also have un unremitting focus on tackling school failure, immediately after a school has been judged by Ofsted to require special measures or significant improvement'.
In preparing a statement of action on such schools, local authorities 'will need to consider how best to involve parents at that school'. The DfeS is encouraging authorities to appoint Parents Champions.
The guidance adds that in some cases, 'it will be necessary to close a poorly performing school'.
The DfeS plans to consult stakeholders over the next few months, leading to a revised document as and when the bill becomes law.
'We are particularly keen to exemplify the statutory provision with real examples of innovative and effective practice that we know is going on across the country to support improved standards in schools.'