On Friday, army weapons experts and scores of troops were deployed to Salisbury to assist in the investigation.
British officials say there is not a public health threat but some residents have become alarmed by the site of investigators wearing extensive hazardous material protection gear.
Investigators are said to be probing whether Yulia could have brought the toxin with her from Russian Federation as a present from friends for her father.
A Russian spy-turned-model who was part of swap with the poisoned double agent Sergei Skripal has condemned him as a "traitor" and hit out at Britain's reaction.
Mrs Rudd had earlier visited Salisbury and the hospital where DS Bailey is receiving treatment.
After chairing a meeting of the United Kingdom government's emergency response committee, Amber Rudd said more than 250 counter-terrorism police were involved in the investigation, which was proceeding with "speed and professionalism".
Earlier Friday, members of the armed forces removed a police vehicle used in the initial response from Salisbury district hospital.
On Saturday screens and tents were erected across the area as troops removed vehicles linked to the poisoning to test for deadly nerve agents. "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.
Western intelligence services consider Russian Federation a leading suspect based on previous attacks that used a similar substance and method, a Western intelligence official told CNN. Does the West needs proof to blame Russia?'
Russian Foreign Minister Sergei Lavrov dismissed Britain's warnings of retaliation were propaganda and not serious.
Rudd led Saturday's talks and briefed senior cabinet ministers, including Foreign Secretary Boris Johnson, on the police investigation. The spokesman said Johnson's comments were an attempt to politicize the affair, and attacked the media for aiding the United Kingdom government's efforts.
Over 250 members of the United Kingdom counterterrorism police were working on the investigation into the poisoning of the Russian-born double agent Sergei Skripal.
Ms Petrova said her friend had got on well with Mr Skripal but had "not been drawn to England" when her father was handed over by Russian Federation in an exchange in Vienna in 2010. In 2010, he was released from prison and sent to Britain as part of a spy exchange with Western agencies.
Suspicion is mounting that Russian Federation carried out the attempt on their lives as an act of revenge against the former intelligence officer, who was convicted in 2006 of selling state secrets to MI6. Skripal's wife, Lyudmila, 59, died of cancer in 2012. Police have sealed off both graves, the UK's Press Association reported, but it was unclear on Friday why.
A British public inquiry found the killing of Litvinenko had probably been approved by Russian President Vladimir Putin and carried out by two Russians, Dmitry Kovtun and Andrei Lugovoy. At the time, the Russian Foreign Ministry dismissed the United Kingdom investigation as politically motivated.
He said: "There obviously are some indications the officer, and I'm very sorry that he has been injured, has actually been to the house, whereas there was a doctor who looked after the patients in the open who hasn't been affected at all".
Marina Litvinenko said Russians living in the United Kingdom feel "insecure and very unsafe" and that the United Kingdom government should do more to protect those who have claimed political asylum.