Former double agent Skripal, 66, and Yulia, 33, have been in hospital in a critical condition for a week.
"The two victims remain in hospital and they're critical but stable," Rudd told reporters.
In Salisbury, normally a quiet city, military vehicles and troops in protective suits and gas masks were seen working at several of the sites associated with the Skripal investigation. At an ambulance station a short distance from the city centre, troops in light grey overalls, purple gloves and gas masks covered ambulances with black tarpaulins as they prepared to remove them. At the hospital where the Skripals were being treated another team used an army truck to remove a police car.
Rudd told reporters that Nick Bailey, a police officer who became unwell after taking part in the early response to the attack, remained seriously ill but was talking and engaging with his family. "He does not consider himself a 'hero', he states he was merely doing his job," a police statement said.
Rudd said more than 250 counter-terrorism police, from eight out of Britain's 11 specialist units, were involved in the investigation.
There was also a flurry of activity at the cemetery in Salisbury where Skripal's wife and son are buried, with forensic teams active in several parts of the site. Skripal's son, Alexander, died in July last year at the age of 43. British media reported that he died while in St Petersburg, Russia. Skripal's wife, Liudmila, died of cancer at 60, in 2012.