Home Secretary Suella Braverman is still pushing for restrictions on the use of tents by rough sleepers in England and Wales.
The proposal was not in the King's Speech setting out the government's priorities for the year ahead.
But a source close to Mrs Braverman insisted the idea had not been dropped.
Downing Street said it would not speculate on whether the proposal would eventually be included in the Criminal Justice Bill.
The bill - which was in the King's Speech - includes proposed new powers to tackle "persistent, nuisance, and organised begging".
It is designed to replace the 1824 Vagrancy Act, which makes begging and rough sleeping a criminal offence in England and Wales.
One senior government source told the BBC the Criminal Justice Bill had been due to start its journey into law on Wednesday, but its introduction in the Commons had been delayed by discussions about whether to include the tents idea.
Some figures in government also have concerns the measures may face legal challenges.
Mrs Braverman wants the bill to include fines for rough sleepers who have been warned by police about causing a nuisance, such as by refusing to move their tents from shop doorways.
It would be aimed at those who "choose to live in tents" and had refused offers of help to get off the streets or enter drug treatment, Mrs Braverman's spokesman told the BBC.
It would also include civil penalties for charities that supply tents to rough sleepers identified by police as having caused a nuisance.
Mrs Braverman's announcement at the weekend - in a series of posts on X - that she wanted to restrict the use of tents sparked a backlash from homeless charities and opposition parties.
Some Conservative MPs have also criticised the home secretary's proposal, with Natalie Elphicke saying in a post on X: "In all my years of helping people who are homeless, in cities like London and Manchester as well as my own local area in Dover and Deal, at no time, ever, has anyone said the answer lies in the removal of tents."
In her statement, the home secretary said the government would always support those who are genuinely homeless, but added: "We cannot allow our streets to be taken over by rows of tents occupied by people, many of them from abroad, living on the streets as a lifestyle choice."
Unless action is taken, she said, "British cities will go the way of places in the US like San Francisco and Los Angeles, where weak policies have led to an explosion of crime, drug taking and squalor."
Her Conservative colleague, Justice Secretary Alex Chalk, appeared to distance himself from Ms Braverman's comments in an interview with Sky News, saying he would "take a different approach".
But he stressed that they were both in agreement on the need to address factors that "entrenched" rough sleeping such as "mental health issues, substance abuse problems, relationship breakdown, loss of a job and so on".
Mrs Braverman's planned crackdown on tents was due to be included in the King's Speech, according to press reports.
But Mrs Braverman's spokesman told the BBC it had always been the plan to introduce it later, as part of of the Criminal Justice Bill.
Downing Street said further details would be set out when the bill was published.
The prime minister's spokesperson said: "We've said that no-one should be criminalised for having nowhere to live and we are repealing the outdated Vagrancy Act.
"We want to go as far as possible to ensure that those who are vulnerable can get the support they need and obviously at the same time cracking down on anti-social, intimidating or indeed criminal behaviour."
Polly Neate, chief executive of housing charity Shelter, said: "The home secretary needs to listen to the public outcry and educate herself on the true causes of homelessness, rather than continuing to pick on people who are already living in some of the most difficult, dangerous, and deadly conditions.
"You don't tackle homelessness through punitive policies that criminalise people for trying to stay warm.
"The government must start protecting people from homelessness instead of punishing them for it and unfreeze housing benefit in its forthcoming Autumn Statement."
There was no mention of tents in the official background notes on the Criminal Justice Bill, which were published earlier on Tuesday.
BBC Newsnight reported on Monday night that we would not see government action on tents "for now".
The home secretary's ideas on tents were "still undergoing scrutiny", Nick Watt was told.