Khalid Mohamed Omar Ali, 27, was arrested on suspicion of offences under the Terrorism Act and possession of offensive weapons on 27 April.
He was detained as part of an intelligence-led operation after a concerned family member is believed to have contacted the police.
Police said he remains in custody and can be questioned until 11 May.
It comes after a warrant of further detention was granted at Westminster Magistrates' Court on Wednesday.
Mr Ali is thought to be a UK national - but born overseas - and to have gone to school in Tottenham, north London.
He was arrested in Parliament Street, at the junction with Parliament Square, following a stop and search as part of an ongoing operation, police said.
Police have been granted another week to question a terror suspect arrested near the Houses of Parliament.