He remains in a serious condition although he is now able to talk, Rudd said.
"In terms of further options, that 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.
Skripal and his daughter remain in critical condition in Salisbury.
About 180 troops including some with chemical expertise have been sent to the city to remove ambulances and other vehicles involved in the incident and other objects.
Police have carried out further searches at Mr Skripal's home with forensic checks have been carried out on his auto.
Skripal and his daughter Yulia were found unconscious on a bench in Salisbury on Sunday.
Britain has said it will respond robustly if evidence shows Russian Federation was behind the attempted murder.
Rudd said 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 said Russian Federation was ready to assist "any investigation" but that it was "not necessary to hurl unfounded accusations on TV".
The Times newspaper said British officials were talking to their USA and European counterparts about a co-ordinated retaliation, which could include "diplomatic, economic and military measures" if Moscow was behind the attack.
On Saturday, investigators dressed in protective suits were seen around her grave with a brightly coloured gurney placed nearby, while workers erected a barrier at the entrance to the cemetery where Lyudmila was buried following her death in 2012. He was convicted in Russian Federation of spying for Britain before he was granted refuge in the UK after a high-profile spy swap in 2010 between the United States and Russian Federation.
However, he said, "there are not 101 likely offenders", apparently a reference to the difficulty in producing nerve agent, which would limit the number of suspects with the ability to carry out the attack.
On Friday, Russian Foreign Ministry Sergey Lavrov dismissed allegations of Russian involvement as "propaganda".
Foreign Secretary Johnson has noted the "echoes" with the 2006 poisoning in London of former Russian spy and Kremlin critic Alexander Litvinenko, which Britain has blamed on Russia.
DS Bailey was one of the first at the scene when the pair were found slumped in The Maltings on Sunday.
The investigation into the nerve agent attack on a former Russian spy in the United Kingdom has broadened as police revealed that 21 people had received medical attention in the aftermath of the incident.
The authorities did not provide details, saying only that they had not exhumed any bodies, but the forensic activities at the London Road Cemetery intensified speculation about the poisonings.
On Friday, John Glen, a member of Parliament for Salisbury, praised the calm response of the city's residents to "an unprecedented occurrence in our country's history" but acknowledged that some were demanding "decisive action". "If you really need help from Russian Federation, then we will be ready to consider such a possibility, if we do have relevant data", he said, speaking in Addis Ababa, Ethiopia.
A British public inquiry found Russia was responsible for Litvinenko's killing, and Russian President Vladimir Putin probably approved it.