The two men alleged to have been behind the March nerve agent poisoning - Alexander Petrov and Ruslan Boshirov - have been identified by the UK as members of the GRU, Russia’s military intelligence service.
Security Minister Ben Wallace said Mr Putin had a strong grip over his state which “controls, funds and directs” the GRU.
British and Russian officials will come face-to-face as the UN Security Council discusses the attack in New York.
Prime Minister Theresa May told MPs it was carried out by two GRU agents and sanctioned at a “senior level” in the Russian state.
Mr Wallace went further, telling BBC Radio 4’s Today that Mr Putin bore responsibility for the actions of his administration.
“Ultimately he does insofar as he is President of the Russian Federation and it is his government that controls, funds and directs the military intelligence - that’s the GRU - via his minister of defence,” Mr Wallace said.
“The GRU is, without doubt, not rogue, it is led, linked to both the senior members of the Russian general staff and the defence minister and, through that, into the Kremlin and the president’s office.”
The PM told MPs on Wednesday the UK would push for new sanctions against Russians responsible for cyber attacks, additional listings under the existing regime and promised to work with intelligence allies to “counter the threat posed by the GRU”.
Mr Wallace said the UK would “use whatever means we have within the law and our capabilities” to “push back the Russian malign activity”.
Asked whether there would be retaliation for Russia’s activities, particularly in cyber space, Mr Wallace said: “We do all the time, but we retaliate in our way.
“We are not the Russians, we don’t adopt the sort of thuggish, destructive and aggressive behaviour that we have seen.
“We choose to challenge the Russians in both the overt and the covert space, within the rule of law and in a sophisticated way.”
As a permanent member of the Security Council, Russia will be represented at Thursday’s meeting - and called on by Britain to update members on progress in the Salisbury investigation - alongside UK allies such as the US and France.
Mrs May has been in contact with US President Donald Trump and other leaders as she attempts to build an international alliance in support of her stance.
The developments came amid claims that President Trump was “reluctant” to expel 60 Russian diplomats following the Salisbury poisonings in March.
An anonymous article in the New York Times, attributed to a “senior official in the Trump administration”, claimed that the President “complained for weeks about senior staff members letting him get boxed into further confrontation with Russia ... But his national security team knew better - such actions had to be taken, to hold Moscow accountable”.
Washington was gripped by speculation over the author of the column, which painted a damning portrait of the President’s “amorality” and his “impetuous, adversarial, petty and ineffective” leadership style, and claimed that many members of his own administration were secretly working to rein him in.
President Trump himself suggested in a series of angry tweets that the anonymous official may have committed treason, or may even be fictitious.
Australia on Thursday said it was in “lock step” with the UK on the importance of holding Russia to account over the “heinous” attack, although it is not currently a council member.
Former GRU officer Sergei Skripal and his daughter Yulia were left critically ill after being exposed to the military grade nerve agent Novichok in March.
The alleged perpetrators were identified in a dramatic joint police and Crown Prosecution Service press conference.
Detectives believe it is likely the pair, thought to be aged around 40, travelled under aliases and that Petrov and Boshirov are not their real names.
Prosecutors deem it futile to apply to Russia for the extradition of the two men, but a European Arrest Warrant has been obtained and the authorities are also seeking the assistance of Interpol.
Detectives believe the front door of Mr Skripal’s Salisbury home was contaminated with Novichok on March 4.
Mr Skripal, 67, and his daughter were found unconscious on a bench in Salisbury city centre the same day and spent weeks critically ill in hospital.
Metropolitan Police Assistant Commissioner Neil Basu also confirmed officers have now linked the attack on the Skripals to events in nearby Amesbury four months later.
In the second incident, Dawn Sturgess, 44, and her partner Charlie Rowley, 45, were exposed to the same nerve agent used in Salisbury.
Ms Sturgess died in hospital in July, just over a week after the pair fell ill.
Mr Putin’s spokesman Dmitry Peskov said that Mrs May’s accusations are “unacceptable” and that “no-one in the Russian leadership” has anything to do with the poisoning, while foreign ministry spokeswoman Maria Zakharova accused the UK and USA of a “witch hunt” against Russia.
The Russian Embassy in the UK used its Twitter account to post a series of messages aimed at undermining the credibility of the UK investigation - including comparisons to the intelligence evidence used to build the case for the 2003 invasion of Iraq.