Education Secretary Ruth Kelly insists she can win over Labour MPs opposed to the party's school reforms in England, despite criticism from Lord Kinnock.
The ex-Labour leader said "trust" schools, with more say over admissions, could "shatter" the education system.
The Tories threatened to drop their backing for the reforms if Labour "retreated" to Lord Kinnock's position.
Ms Kelly insisted she would not need Tory votes as Labour MPs backed the "vast majority" of her proposals.
She said: "This is a very, very complex area. I think there is big misunderstanding among certain of my colleagues.
"But actually in the talks that I have been having with backbenchers over the last couple of months, those concerns have narrowed down quite substantially to a couple of areas."
Lord Kinnock's comments are being seen as an unprecedented attack by the normally loyal ex-party leader on the current Labour leadership.
They come as Tony Blair is struggling to persuade his party to support his flagship education reforms - seen as crucial to the success of his third term.
H said autonomous trust schools, some of them run by businesses or faith groups, could create a "dreadful shattering of the school system".
"If in an area you get a school of that kind its impact is felt on every school, every pupil, every family in the area," he warned.
More than 90 Labour backbenchers support an "alternative" version of the government's plans, which calls for academic selection to be ruled out.
Downing Street insisted on Friday that this practice was already "illegal", although selection by aptitude was allowed - a distinction criticised as meaningless by the Conservatives.
David Chaytor, a leading Labour rebel, said there were "a dozen ways in which schools have selection by ability in a covert way, and that has to be tackled".
Academic selection was not forbidden in the Department for Education and Skills' code of practice for admissions, he added.
A draft report by the Commons education select committee is also thought to raise concerns about government plans.
According to The Times, it calls for local authorities to gain powers to ensure trust schools take their "fair share" of poor and disadvantaged pupils.
Labour rebels, who fear greater freedom from local authorities could mean a "back-door" return to academic selection at age 11, want a national code on admissions to be made legally binding.
Conservatives have promised to support trust schools.
Shadow education secretary David Willetts told BBC Radio 4's Today programme it was important to "make it easier for good schools to expand" and that Prime Minister Tony Blair should not "retreat" towards Lord Kinnock's position.
The government is due to publish its final plans in an Education Bill next month.