The circumstances of the Whitehall arrest would suggest the suspect may have been under some form of surveillance before he was detained.
The suspect was arrested by armed police in Whitehall
Police have described the operation as "intelligence-led" and reports have suggested security services were tipped off by members of his Muslim family.
Met Police deputy assistant commissioner Neil Basu gave an update on the investigation on Friday morning.
He said: "In Whitehall, a 27-year-old man was arrested by armed officers from the Met's Specialist Firearms Command, who stopped and searched him as part of an ongoing counter terrorism investigation.
"He remains in our custody having been arrested for Terrorism Act Offences and possession of offensive weapons and there are two ongoing searches at addresses in London as part of that investigation.
A forensic investigator recovers a knife from the scene
Images from the scene showed three knives on the ground close to a brown rucksack, and an officer in forensic overalls could be seen taking photographs of the weapons.
The bearded suspect was taken to a south London police station where he is being held under the Terrorism Act.
The arrest took place at the Parliament Street junction with Parliament Square, close to the scene of last month's terror attack which killed five people, including police officer Keith Palmer, on 22 March.
Prime Minister Theresa May was not at Number 10 at the time of Thursday's incident.
The suspect, believed to be from London, was wrestled to the ground on a traffic island by police.
The man was detained during a stop and search as part of an ongoing operation
He was handcuffed, with his arms behind his back, and one of his hands appeared to be wrapped up in a bandage as four officers stood next to him.
A builder working on the road nearby said: "I saw the police officers catch him. They caught him and got him on the ground."
Asked if the suspect was waving knives, acting aggressively or shouting, the witness said: "No."
Another witness said the suspect was "very calm" as he was arrested, and did not struggle as he was held on the ground.