A lawyer said the detained man, David Miranda, had begun legal action against the government, calling his detention unlawful and seeking assurances that British officials would not share the "sensitive, confidential journalistic material" seized from Miranda with anyone else.
Police used a contentious anti-terrorism law to detain Miranda, the civil partner of Guardian newspaper journalist Glenn Greenwald, on Sunday. Greenwald has published stories about U.S. and British surveillance programs based on documents leaked by Snowden, who has been granted temporary asylum in Russia.
Miranda was held for nearly nine hours - the maximum allowed by law - and had a computer and other electronic equipment confiscated.
Miranda, a 28-year-old university student, was traveling home to Brazil after visiting Germany, where he met with Laura Poitras, a U.S. filmmaker who has worked with Greenwald on the NSA stories. Greenwald said Miranda was carrying materials between the two, but didn't specify what they were.
"The government and the police have a duty to protect the public and our national security," the Home Office said in a statement.
"If the police believe that an individual is in possession of highly sensitive stolen information that would help terrorism, then they should act and the law provides them with a framework to do that," it said.
"Those who oppose this sort of action need to think about what they are condoning."
The Guardian and civil liberties groups have condemned the use of counter-terrorism legislation to detain a journalist's partner.
London law firm Bindmans said it was representing Miranda and had written to police and the government seeking assurances that there would be no "inspection, copying, disclosure, transfer, distribution or interference, in any way, with our client's data pending determination of our client's claim."
The letter, released to The Associated Press, said Miranda "assists Mr. Greenwald in his legitimate journalistic work and was doing so when he was detained."
It said it was seeking "a declaration that the decisions to detain our client, question him under pain of criminal sanction, and seize his property under Schedule 7 were wholly unlawful."
Authorities should return a "mobile phone, laptop, memory sticks, smart-watch, DVDs and games consoles" taken from Miranda, the letter said.
"These items contain sensitive, confidential journalistic material and should not have been seized," it said.
The government has claimed the decision to stop Miranda was made by police, although White House spokesman Josh Earnest said Monday that Britain had tipped off the U.S. government that Miranda would be detained.
Prime Minister David Cameron's office said Tuesday that his office had been "kept abreast of the operation," but was not involved in the decision to stop Miranda.
Britain's opposition Labour Party demanded to know whether the government was aware of the operation in advance
"The home secretary needs to tell us whether she or the prime minister were informed or involved in this decision," said Labour law-and-order spokeswoman Yvette Cooper. "Is it really possible that the American president was told what was happening but the British prime minister wasn't?"
The Home Office said it could not "comment on the specifics" of an ongoing police inquiry.
The piece of legislation used to stop Miranda - Schedule 7 of the Terrorism Act - is especially contentious because it allows police to stop people passing through airports without suspicion they have committed an offense. It allows people to be held for up to nine hours, although the vast majority of stops last an hour or less.
After pressure from civil libertarians, the government is in the process of reducing the time limit to six hours and imposing other safeguards, but critics say the measure remains too broad and is open to abuse.
The Metropolitan Police said the use of Schedule 7 to stop Miranda "was legally and procedurally sound."
Guardian editor Alan Rusbridger characterized the detention of Miranda as part of a campaign of official intimidation against the newspaper since it began publishing stories based on Snowden's leaks in June. The articles revealed details of surveillance of electronic communications carried out by U.S. and British spies.
Rusbridger said senior government officials had demanded the return or destruction of Snowden's material, eventually threatening legal action if the newspaper did not comply.
Rusbridger told the BBC Tuesday that it became clear that "the government was on the verge of launching legal action against the Guardian."
He said that faced with that threat, he agreed to destroy hard drives containing Snowden's material at The Guardian's London offices, while staffers from British eavesdropping agency GCHQ watched.
Rusbridger said The Guardian had other copies of the material that was destroyed.
Kirsty Hughes, chief executive of Index on Censorship, said that "using the threat of legal action to force a newspaper into destroying material is a direct attack on press freedom in the U.K."