Greenwald has written about NSA surveillance programs based on files disclosed by Snowden, who now has temporary asylum in Russia. The Obama administration wants Snowden sent back to the United States to be tried for the leaks.
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.
A spokesman for Prime Minister David Cameron said that "Schedule 7 forms an essential part of the U.K.'s border security arrangements," but added that it was for the police to decide "when it is necessary and proportionate to use these powers."
Brazil's Foreign Minister Antonio Patriota and his British counterpart, William Hague, spoke by phone Monday, the British Embassy in Brasilia said in a statement.
"They agreed that Brazilian and U.K. officials will remain in contact on this issue. This remains an operational matter for the Metropolitan Police," British Ambassador Alex Ellis said in an emailed statement.
The Guardian said that it paid for Miranda's flights but that he was not an employee of the newspaper.
"As Glenn Greenwald's partner, he often assists him in his work," the newspaper said in a statement. "We would normally reimburse the expenses of someone aiding a reporter in such circumstances."
In an email Monday to The Associated Press, Greenwald said that he needed material from Poitras for stories he was working on with her relating to the NSA, and that he had things she needed.
"David, since he was in Berlin, helped with that exchange," Greenwald wrote.
Greenwald didn't specify what material Miranda might have been carrying. He said that only he and Poitras "have copies of the full archives of NSA documents which Snowden gave to journalists."