In a statement, Reid she had never seen anything to make her suspect her husband had “broken any law”, adding that she was “not part of” his business activities.
The Welsh Conservatives called for a statement from First Minister Eluned Morgan on the arrests, saying “we need to ensure that Wales is not a weak link when it comes to the UK’s national security” and said there were questions for Morgan to answer.
The request was rejected by the Senedd’s Presiding Officer, the Llywydd Elin Jones.
The Welsh government said it does not comment on live police investigations.
Hours before Reid’s statement, the Met Police said a 39-year-old man had been arrested in London.
The force added that a 68-year-old man had been detained in Powys, and a 43-year-old man had been arrested in Pontyclun, Rhondda Cynon Taf.
Police said all three have been accused of assisting a foreign intelligence service under section three of the National Security Act, which was introduced in 2023 to target suspects accused of working against UK interests.
The Met said they were supported by counter-terror police in Wales and in Scotland.
An address linked to one of the arrested men in Pontyclun has been searched.
A car outside was also searched and photographed.