Skripal, 66, and daughter, Yulia, 33, are fighting for their lives after they were attacked with a nerve agent in Salisbury, Wilts.
A police officer who needed intensive care after attending the scene of a poisoning in Salisbury has said he does not consider himself a "hero" and he was "merely doing his job".
Russian Federation was not involved in the attempted murder of an ex-spy and is willing to help with a United Kingdom inquiry, the country's foreign minister has said.
They remained in critical condition in a hospital Friday, poisoned with what authorities say is a nerve agent.
On Friday, police called in about 180 marines, soldiers and air force personnel with expertise in chemical weapons, decontamination and logistics to help with the probe and to remove vehicles that might be contaminated.
Police have also cordoned off Skripal's modest home in Salisbury, about 130km from London, and erected forensic tents in the garden.
During the attempted poisoning of former Russian intelligence officer Sergei Skripal in the British city of Salisbury, injured 20 people, including the daughter of Yulia Skripal and Sergeant nick Bailey. "It's too early to say how far and wide this investigation will stretch".
Russian Federation has denied responsibility for the attack, which comes seven years after Mr Skripal was released from the country as part of a spy swap with the US.
Skripal's daughter is thought to be one of the few members of his immediate family still alive after his wife, Lyudmila, and son Alexander died in recent years.
"We will have to wait until we're absolutely clear what the consequences could be, and what the actual source of this nerve agent has been", Rudd said in Salisbury.
Former Metropolitan Police Commissioner Lord Blair said the "extraordinary attack in Salisbury" is a good reason to investigate whether there is a pattern of former British intelligence collaborators dying in the UK.
Acting Chief Constable of Wiltshire Police, Kier Pritchard, said he had been to visit DS Bailey.
With police also hurt in the attack, pressure is intensifying on Prime Minister Theresa May to find and punish the culprits.
Russian Foreign Minister Sergei Lavrov has categorically denied any Kremlin involvement, dismissing it as baseless "propaganda".
Authorities are racing to identify the nerve agent used against the 66-year-old Skripal, who came to Britain in a spy swap in 2010, as politicians warned it showed the hallmarks of an attack by Russian Federation.
Russian Federation is fighting a new Cold War against Britain which people need to be aware of, an MP has warned.
Local convenience store manager Ebru Ozturk, who saw Skripal at his shop just days before the incident, told CNN that he was a "kind customer" who would usually come in once a week and buy Polish-smoked bacon and scratch-and-win lottery cards.
Sunday's attack has drawn comparisons with the case of ex-Russian spy Alexander Litvinenko, who was poisoned with polonium at a London hotel in 2006.
"You can not tolerate a government assassination on British soil - it is absolutely beyond the pale and needs a reaction", he said.
A British public inquiry found Russia was responsible for Litvinenko's killing, and Russian President Vladimir Putin probably approved it.