No 10 was "kept abreast" of the decision to detain David Miranda, the partner of Guardian journalist Glenn Greenwald, a spokesman has said.
Mr Miranda was held at Heathrow for nine hours on Sunday, while in transit from Germany to Brazil.
He has launched a legal challenge over the police's use of anti-terror laws to detain him and seize his property.
But Home Secretary Theresa May said the police must act if someone had "highly sensitive stolen information".
Mr Miranda, a 28-year-old Brazilian national, was held at Heathrow on his way from Berlin to Rio de Janeiro where he lives with Mr Greenwald. The Guardian said he had been carrying "journalistic materials" but was not an employee of the newspaper.
Mr Greenwald has broken most of the stories about state surveillance based on the leaks from fugitive Edward Snowden, who used to work at the US National Security Agency.
Mr Miranda said he was held in a room and questioned by six agents about his "entire life". They confiscated his laptop, an additional hard drive, two memory sticks, a mobile phone, a smart watch and a video games console, his lawyers said.
He was required to divulge the passwords to his personal computers, phone and encrypted storage devices, they added.
In Germany, Mr Miranda had been staying with US film-maker Laura Poitras, who has also reportedly been working on the Snowden files with the Guardian. DVDs of two of her films - The Oath and My Country, My Country - were also seized at Heathrow, the lawyers added.
Mr Miranda was detained under schedule 7 of the Terrorism Act 2000. This allows police to hold someone at an airport, port or international rail station for up to nine hours for questioning about whether they have been involved with acts of terrorism.
He is now taking action to challenge the legality of his detention, and to try to prevent the police from examining the electronic items they seized from him.
His law firm Bindmans have written to the home secretary and Met Police commissioner for assurances "there will be no inspection, copying, disclosure, transfer, distribution or interference, in any way, with our client's data pending determination of our client's claim".
Guardian editor Alan Rusbridger wrote earlier that the transit lounge at Heathrow was "a dangerous place to be" as a detention under section 7 offered "none of the checks and balances that apply once someone is in Britain proper".
The legal challenge would determine whether it was "permissible for government to use powers to be able to get material from journalists" without enabling them "to argue their case before a court as to why they shouldn't have to answer questions or give up that material", Mr Miranda's lawyer Matthew Ryder, a barrister at Matrix Chambers, added.
The UK's independent reviewer of terrorism legislation, David Anderson QC, has said the length of detention was "unusual" and will meet police later.
'Briefed in advance'
But the home secretary said: "I think that it's absolutely right that if the police believe that somebody is in possession of highly sensitive stolen information that could help terrorists, that could risk lives, or lead to a potential loss of life, that the police are able to act, and that's what the law enables them to do."
She continued: "I was briefed in advance that there was a possibility of a port-stop of the sort that took place.
"But we live in a country where those decisions as to whether or not to stop somebody or arrest somebody are not for me as home secretary, they are for the police to take."
A Home Office spokesperson previously said: "Those who oppose this sort of action need to think about what they are condoning."
And Scotland Yard maintained the detention was "legally and procedurally sound", and had been subject to a "detailed decision-making process".
It added that "contrary to some reports, the man was offered legal representation while under examination and a solicitor attended."
Conservative MP Mark Pritchard also defended the police's actions.
"It may have inconvenienced the Guardian and those that work directly or indirectly for the Guardian," he told BBC Radio 4's The World at One.
"But the fact is they had concerns that there may have been somebody carrying sensitive material that may have directly or indirectly undermined our national security. And I'm glad the police took the action they did."
The US government said on Monday it had been given the "heads up" before Mr Miranda's detention.
Brazil protested to the UK government that the detention was "unjustifiable".
Mr Rusbridger also said "senior Whitehall figures" had previously put pressure on the Guardian as it prepared to publish details of Mr Snowden's material - threatening to injunct it.
He said he was then told he had to destroy, or hand over to the authorities, a computer containing material which had not yet been published.
But the No 10 spokesman told the BBC that it was "complete rubbish" that they had tried to prevent publication of the revelations.