The couple poisoned by Novichok were exposed to the substance after handling a contaminated item, say police.
Charlie Rowley, 45, and Dawn Sturgess, 44, collapsed at a house in Amesbury, Wiltshire, on Saturday and remain critically ill.
Home secretary Sajid Javid said the nerve agent was the same as that used on ex-Russian spy Sergei Skripal and his daughter in March.
Russia said Theresa May’s government was subjecting them “to hell”.
Police have not identified the item handled by the couple.
Mr Javid accused Russia of using Britain as a “dumping ground for poison” after the second incident involving the nerve agent.
Russian foreign ministry spokeswoman Maria Zakharova urged police not to be led by the “dirty political game” and said she was confident London would have to apologise to Russia.
Debbie Stark, south west deputy director from Public Health England said the risk to the public of further poisoning incidents “remains low”.
Police have set up a helpline for anyone who needs further advice: 0800 092 0410 or 0207 158 0124.
In a statement to MPs, Mr Javid said: “It is now time that the Russian state comes forward and explains exactly what has gone on.”
He said the “strong working assumption” was that the couple came into contact with Novichok in a different location to the sites which had been part of the clean-up operation in near-by Salisbury after the Skripal poisoning.
“It is completely unacceptable for our people to be either deliberate or accidental targets, or for our streets, our parks, our towns, to be dumping grounds for poison,” he added.
He said he could not rule out the possibility that the Novichok found in Amesbury was from the same batch used in the Salisbury attack and that scientists “will be looking into that.”
BBC security correspondent Gordon Corera said the most likely hypothesis was that the Novichok was left over from the attack on the Skripals.
Earlier, Mrs May said it was “deeply disturbing” to see two more people exposed to Novichok in the UK, and the police would leave “no stone unturned in their investigation”.
Shadow home secretary Diane Abbott said British streets must not be allowed to become “killing fields for state actors”.
On Saturday, paramedics were called twice to a house in Muggleton Road in Amesbury – first at 11:00 BST after Ms Sturgess collapsed, then later the same day, after Mr Rowley also fell ill.
Wiltshire Police said it was initially thought the two patients had been using heroin or crack cocaine from a contaminated batch of drugs.
They explained that this assessment was based on items located at the address where the couple fell ill, information from a friend of the pair and the “initial medical diagnosis”.
In the early hours of Wednesday police declared a “major incident” after revealing the couple had been exposed to an “unknown substance”.
By late that evening, Scotland Yard said Novichok was to blame following analysis at the defence research facility at Porton Down, Wiltshire.
Salisbury District Hospital’s chief executive Cara Charles-Barks said the couple are “extremely unwell” and remain in a critical condition.
What do we know about the couple’s movements?
Partners Charlie Rowley and Dawn Sturgess spent Friday afternoon and evening visiting shops in Salisbury, the city where Mr Skripal and his daughter were poisoned.
The following day Ms Sturgess, who is understood to be a mother of three, was taken away on a stretcher by an ambulance crew.
Her friend Sam Hobson said she had appeared to have a fit and was “foaming at the mouth”.
Shortly after, Mr Rowley started “rocking against the wall”, said Mr Hobson.
“His eyes were wide open, glazed and pinpricked, and he was sweating, dribbling and making weird noises.”
Mr Hobson said the police and firefighters were in “hazard suits” and “cordoned it all off”.
Ms Sturgess’ father Stephen, 65, told The Times the family found out from TV news that she may have been poisoned by a nerve agent.
“We heard from the hospital on Sunday, and we gave them Dawn’s GP details but we didn’t hear anything from the police.
“We know as much as the next person in the street. We actually called the police station for information.”
- What are Novichok nerve agents?
- Russian spy: What happened to the Skripals?
- Amesbury poisoning: What we know so far
Natalie Smyth from Amesbury said: “I’m furious that it took four days for them [police] to even mention it could have been Novichock.”
“Were they lying to us about it being drug related?”
How did it happen?
The most likely hypothesis was that the Novichok was left over from the attack on the Skripals, says BBC security correspondent Gordon Corera.
Mr Javid said this was the “leading line of inquiry”.
Metropolitan Police Assistant Commissioner Neil Basu said they could not confirm whether the nerve agent came from the same batch but the possibility was “clearly a line of inquiry”.
There was nothing in the couple’s background to suggest the pair had been targeted, he said.
His officers are examining the couple’s movements to determine where they were poisoned.
So far no contaminated items have been found and the police say they have no idea what the nerve agent was contained in.
Chemical weapons expert Richard Guthrie said it was possible that the couple came across the Novichok which poisoned the Skripals after it had been disposed of “in a haphazard way”.
Novichok poisoning: Salisbury reacts to fresh case
The revelation that two more people have been exposed to the nerve agent Novichock has shocked people in Salisbury.
Residents have experienced months of disruption and anxiety since the poisoning of Sergei Skripal and his daughter Yulia in March.
Now many are wondering whether, despite a clean-up operation, their city is safe?
Are others at risk?
Although the risk to the public remains low, Public Health England (PHE) have advised those who were in the areas now cordoned off from 22:00 BST on Friday to wash their clothes and wipe down personal items.
Clothing that cannot be washed should be double-bagged and owners should await “further instructions”.
Debbie Stark from PHE said areas of Salisbury that have already been cleaned as part of the Skripal incident – such as the Maltings shopping centre – are safe.
Residents at John Baker House, the supported housing where Ms Sturgess is believed to have been staying, have been evacuated and told they will have to be rehoused.
The police warned members of the public against picking anything up if they didn’t know what it was.
Sites in Amesbury and Salisbury believed to have been visited by the couple before they fell ill have been cordoned off as a precaution, including a church, park and chemist.
This latest incident is likely to raise fears about the efficacy of a multimillion pound clean-up to decontaminate nine locations across Salisbury after the Skripal poisoning.
What’s been the reaction in Russia?
There have been accusations of the UK persecuting Russia and failing to cooperate.
The Skripal case is still shrouded in darkness, says Russia spokeswoman Maria Zakharova, as she called on Theresa May’s government to stop the “dirty” games.
She says Russia has sent “dozens of offers of cooperation”.
Russian media: ‘Groundhog Day’
By BBC Monitoring
The state media in Russia are deflecting any suggestions of a Russian link to the new poisoning.
Even before it emerged that the Novichok agent was involved, Wednesday night’s primetime TV bulletins sarcastically said it was only a matter of time before Moscow gets the blame.
State-run Rossiya 1 suggested it might have been staged by the British government out of spite over the “fabulous” World Cup hosted by Russia.
NTV – owned by state gas giant Gazprom – called it “another dodgy story” from the Salisbury area, this time aimed at deterring fans from coming to Russia.
Again, it added, the British had offered no detailed evidence: “Boris Johnson and British journalists will think up the rest.”
Channel One accused the UK of “dragging old skeletons out of the closet” to discredit Moscow ahead of President Vladimir Putin’s upcoming summit with Donald Trump.
“Groundhog Day. New Skripals in Salisbury. Really?” said its presenter.
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Amesbury poisoning: Couple ‘handled contaminated item’