He told ITV1's Good Morning Britain: 'Russia's being assertive, Russia's being more aggressive, and we have to change the way that we deal with it because we can't be in a situation in these areas of conflict where we are being pushed around by another nation'.
Suspicion is mounting that Russia 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.
Now, the paranoia in the UK in the Skripal case is reaching massive proportions, with a junior minister calling on London to contact its NATO allies over the incident.
The father and daughter, believed by authorities to have been deliberately targeted, were found slumped on a bench near a shopping center on Sunday afternoon.
More than 240 pieces of evidence have been collected and 200 witnesses have been identified, she said. The UK needs to make clear that Russia will pay a price for this kind of behaviour.
British health authorities said Sunday that small traces of contamination have been found in a restaurant and a pub in the English city of Salisbury, after a Russian ex-spy and his daughter were poisoned with a nerve agent.
Amid hysteria surrounding the mysterious poisoning of Sergei Skripal, Britain is dedicating a significant part of the country's anti-terrorism capacity to look for Moscow's hand in the former Russian double agent's misfortune.
Sally Davies said up to 500 people who had visited The Mill pub and the Zizzi restaurant in Salisbury, southwest England, should wash their clothes and belongings as a precaution.
Meanwhile troops remain on the city's streets.
"It's really important to understand the general public should not be concerned", she said.
But he remains under pressure from the opposition Labour Party and some lawmakers in his Conservative Party to spend more on the over-stretched health system and other services.
The graves were sealed off with plastic sheeting.
Prior to his wife's death, however, she reportedly told police that she feared for her husband's life, the Daily News reported.
A police spokesman declined to comment on the report', Reuters wrote.
The risk to public health remained low and the advice was precautionary, Public Health England said.
Skripal had his sentence cut short and was released from prison in 2010 as part of a spy swap.
A large-scale police investigation is underway in Salisbury as forensics experts wearing protective gear search for clues. It's not known if it happened in a restaurant, a pub, Skripal's house or elsewhere.
Skripal was arrested in 2004 in Moscow and later confessed to having been recruited by British intelligence in 1995.
Access to nerve agents, which are chemical weapons, are tightly regulated, meaning the Salisbury plot would have taken considerable planning to execute. Skripal's wife, Liudmila, died of cancer at 60, in 2012.
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