The government's anti-terror plans have cleared their first hurdle in the Lords and will now go to committee.
Police had recommended 90-day detention without charge
The Terrorism Bill includes plans to raise the time terror suspects can be held without charge from 14 to 90 days.
The bill received an unopposed second reading, as is customary, and will now be considered line-by-line by peers.
MPs voted against the 90-day limit and Home Office Minister Baroness Scotland has said the government will not try to overturn the decision in the Lords.
Police have complained the current 14-day limit for holding suspects without charges does not give them enough time to plough through reams of information before questioning suspects.
MPs instead backed a compromise time limit of 28 days.
Lady Scotland told peers on Monday: "As the home secretary said, the government accepts the decision that the House has taken and we will not be seeking to overturn it in the House of Lords."
The minister said she would abstain on any new vote on the 90-day proposal if other peers tried to change the bill.
Conservative spokesman Lord Kingsland and Liberal Democrat legal spokesman Lord Thomas have said their parties would not seek to amend the 28-day proposal.
However, peers from both parties have said they would try to amend the part of the bill covering the circumstances in which people could be held.
Lord Kingsland said allowing intercept evidence in court and putting more resources into decrypting and interpreting evidence was better than holding suspects for up to 90 days.
But Labour peer Baroness Ramsay and Tory Baroness Park backed the 90-day detention limit.
Meanwhile, the government's independent reviewer of the terror laws, Liberal Democrat Lord Carlile, repeated his view that a "very small number" of terror suspects would have needed to be held for up to 90 days.
He said 28 days was "a modest improvement" on the current limit.
Liberal Democrat peers' leader Lord McNally said Parliament was now considering the sixth set of anti-terrorism laws since 1997.
"Each of the preceding Acts, as does this Bill, ratchets a couple of notches in the loss of hard won civil liberties and hard won freedoms," he said.
Lord McNally said new powers had to be considered to tackle threats but Parliament also had to examine whether current powers had been used effectively.
"Otherwise every terrorist outrage will bring forth another bill," he warned.
But former law lord, Lord Lloyd of Berwick, said he did not believe police had made a case for extending the existing detention time limit.
The Terrorism Bill would outlaw the incitement and glorification of terrorism.
But former Conservative Home Secretary Lord Hurd said: "I would advise the home secretary not to spend too much time pursuing individuals because they delight in saying disgraceful things.
"Obnoxious clerics tend to have good lawyers and the home secretary will find himself wasting a lot of time if he goes down this path too often."
The Association of Chief Police Officers (Acpo) have privately opposed four of the 14 main planks of the Terrorism Bill, according to The Guardian newspaper.
The newspaper says a confidential Acpo assessment of the measures concludes that all risk alienating Muslims.
The four measures opposed by Acpo, the paper says, include: amending human rights laws to get round obstacles to new deportation rules and making the justification or glorification of terrorism anywhere an offence.
They are also reportedly against automatically refusing asylum to anyone linked to terrorism anywhere and banning the alleged extremist group Hizb ut-Tahrir.