Peers have defeated the government over its anti-terror bill, voting by 249 to 119 to ensure all control orders will be made by courts and not ministers.
Opponents to the bill have been told to 'make their minds up'
The government had wanted only the more serious control orders involving house arrest to be overseen by judges.
Among 20 Labour rebels was ex-Lord Chancellor Lord Irvine - Tony Blair's boss when he was studying for the Bar.
MPs will get the chance to look again at peers' amendments when the bill returns to the Commons on Wednesday.
The government had said it would give no more concessions on the bill, but there has been no indication what approach ministers will now take when it comes back before MPs.
The Home Office said: "The government continues to believe that the bill as passed by the House of Commons strikes the right balance between protecting the security of the nation and safeguarding individual liberty.
"The Commons will consider the bill as returned by the Lords."
The BBC's political correspondent Mark Mardell said the language coming out of the Home Office was "pretty mild".
He said: "I am just beginning to wonder whether they will accept this, because that would mollify all of the Liberal Democrat and most of the Labour rebels on this, and then sharpen their divisions with the Conservatives and attack what the Conservatives want to do."
The government tabled new legislation after the Law Lords ruled in December that current provisions for detention without trial were unlawful.
Home Secretary Charles Clarke offered some concessions in a bid to get the bill through quickly.
He agreed to hand over the power to place terror suspects under house arrest to the courts, while resisting attempts to require him to get their approval for less stringent orders.
But peers - including crossbencher and former Met police chief Lord Condon - on Monday backed the Lib Dem amendment extending judicial oversight to all control orders.
Two other Lib Dem amendments also made it through.
One raises the standard of proof for making a control order from "reasonable grounds" for suspicion to a requirement that a judge must be satisfied on the "balance of probabilities" such an order is justified.
The second introduces a requirement for the director of public prosecutions to deliver a statement to the court saying there was not reasonable prospect of a successful prosecution before an order was made.
The Shadow Lord Chancellor, Lord Kingsland said opposition parties would also try to introduce a "sunset clause" on Tuesday, which would see the legislation lapse on 30 November.
Lord Kingsland said: "The speed with which this legislation is going through this House and has already gone through the Commons, I believe, is evidence enough that we need such a clause on the face of the bill."
However, Home Office minister Baroness Scotland said: "The government's view is that a sunset clause would not be appropriate.
"This bill should not be seen as a very short stopgap."
The committee stage of the bill has ended and peers will debate the remaining report and third reading stages on Tuesday.