Education Secretary Ruth Kelly says she believes the Education Bill will pass through the Commons after concessions were made to placate rebel Labour MPs.
The bill, due to be published on Tuesday, is expected to include a ban on schools interviewing for selecting children based on academic ability.
She told BBC One's Sunday AM programme she would retain the right to veto councils' attempts to set up schools.
She said she was "very confident" Labour MPs would support the bill.
But relinquishing the veto is one of the key demands of up to 100 Labour MPs who are threatening to vote against Prime Minister Tony Blair over the bill.
Despite her refusal to back down, Ms Kelly said she believed most Labour MPs would accept the proposals would be good for children and give them their backing.
Labour critics have feared the new bill could set up a two-tier education system by allowing schools to pick the best students to help improve their exam pass rates.
But Ms Kelly said: "There was a fear that schools would use some of their new freedoms in order to manipulate their intake. I have always been completely adamant that that is something that we, that I, that the government would not tolerate.
"We have been completely clear that there can be no new selection by academic ability. In order to make that clear to everybody, so everybody knows there is a clear and transparent and robust system, we are going to write that on the face of the bill."
Ms Kelly said: "Schools which interview will have to stop interviewing.
'Sick and tired'
"For those who are worried that interviews can lead to covert selection, schools will have to stop doing that, so everybody is absolutely clear that this is a system within which parents are choosing schools, not schools choosing parents."
Former Education Secretary David Blunkett told BBC Radio Five Live that asking for Tory MPs' support to pass the bill would be "unfortunate and undesirable".
He said there was a hardcore of between 20 and 25 rebels who would always vote against the government on key issues.
"Most colleagues are sick and tired of that. A lot of those who have been concerned are not only willing to be won over, but wanting to be won over, in terms of seeing that movement has been made on the education front, and it has."