The Wales arrest widens the police probe which detained two suspects in England on Saturday.
Friend Alison Griffiths said the couple - foster parents for nearly 40 years who had taken in up to 300 children, including eight refugees - had an 18-year-old and a 22-year-old staying with them recently.
They are reported to be staying with friends while the search continued Sunday in the suburban town of Sunbury southwest of London.
"A search is taking place at an address in the Newport following the arrest".
The couple are said to be staying with friends for at least the next five days following the police raids, during which surrounding houses were evacuated by counter-terror officers, with residents told they had "one minute" to flee their homes. The man was seen on camera leaving a house which police later searched.
Spanish police arrest Catalan minister during raid
The province of Catalonia's headlong rush towards independence challenges the very roots of Spain's existence as a unitary state. However, Wednesday's communique was a show of support, if not for the independence movement, then at least for the right to vote.
A senior British minister has renewed criticism of U.S. President Donald Trump for tweeting about the police inquiry into the bombing of a subway train in London.
Announcing the threat level was being lowered, Rudd said: "I would urge everybody to continue to be vigilant but not alarmed".
He stressed that intelligence cooperation between the United States and Britain is continuing and helps makes the British people safer. The 21-year-old was held later the same day in Hounslow, west London.
The men, aged 48 and 30, were arrested under anti-terrorism legislation in Newport in Wales, police said in a statement, after a 25-year-old man was arrested in the same city on Tuesday.
A third man has been arrested in connection with the Parsons Green terror attack, Scotland Yard said. 17 Sept 2017 | teenager suspected of being the Parsons Green bomber had been spoken to by police a number of times, neighbours of his foster family claimed today, amid questions over what authorities knew.
And you will have heard consequently the Home Secretary's announcement that the threat level has reduced from Critical to Severe which of course means that an attack is highly likely."Members of the public will be wondering what that means in terms of their travel into work tomorrow".