A man who was poisoned by Novichok has spoken "briefly" to officers trying to find the source of the nerve agent, Scotland Yard has said.
Charlie Rowley, 45, is no longer in a critical condition, Salisbury District Hospital said, after making "further progress overnight".
It comes a day after the hospital said he had regained consciousness.
Dawn Sturgess, 44, who was also exposed to Novichok in Amesbury on 30 June, died on Sunday.
Police are investigating a possible link to the case of Russians Sergei and Yulia Skripal, who were poisoned with the same substance in nearby Salisbury in March.
The UK government has blamed Russia for the incident, but the country's authorities deny any involvement.
Chief Medical Officer Dame Sally Davies said people in the Amesbury and Salisbury area should not "pick up any foreign object which could contain liquid or gel, in the interests of their own safety".
Lorna Wilkinson, Salisbury District Hospital's director of nursing, said Mr Rowley's condition was now serious, but stable.
"Our staff will continue to work hard to provide the care that Charlie needs," she said.
"Charlie still has some way to go to recover, but the progress we've seen so far gives us cause for optimism."
In a statement, Scotland Yard said: "Officers from the investigation team have spoken briefly to Charlie and will be looking to further speak with him in the coming days as they continue to try and establish how he and Dawn came to be contaminated with the nerve agent.
"Any contact officers have with Charlie will be done in close consultation with the hospital and his doctors."
The Met Police's assistant commissioner for specialist operations told a meeting in Amesbury that officers were working on the theory that Ms Sturgess and Mr Rowley had found a container housing Novichok.
Neil Basu said scientific advice suggested that the nerve agent could remain active for decades.
"If it was sealed in a container and it was in a landfill site it would effectively be safe because it would not be touched by anyone and it would last for probably - I've been told by scientists - 50 years," he said.
Police cannot say with certainty that both poisoning incidents in the county are linked, Mr Basu said, but it is a main line of inquiry.
"This is a very rare substance banned by the international community and for there to be two separate, distinct incidents in one small English county is implausible to say the least," he said.
He said scientists at the Defence Science and Technology Laboratory at Porton Down will work hard to determine whether the nerve agents in the two incidents were from the same batch.
But, he warned, it may never be possible to establish a definitive link.
"I would love to be able to say that we have identified and caught the people responsible and how we are certain there are no traces of nerve agent left anywhere in Wiltshire," Mr Basu said.
"But the brutal reality is that I cannot offer you any reassurance or guarantee at this time."
Police are continuing to hunt for a contaminated container which they believe was handled by the pair.
The BBC understands Mr Rowley's flat is regarded as the key location in the search, but Mr Basu added: "The brutal fact is we don't know where they found it.
"I am hoping Charlie recovers, and when he recovers he will be able to tell us and perhaps shed some light on it which will narrow our search dramatically."
Ms Sturgess, 44, lived in Salisbury, and the couple had been in the city before going to Mr Rowley's flat in nearby Amesbury on Friday 29 June.
They both then fell ill on Saturday 30, and Ms Sturgess died eight days later. She had two sons, aged 19 and 23, and an 11-year-old daughter.
Public Health England has offered advice for people who may have visited one of five areas identified by police.
Those locations are Muggleton Road, Boots pharmacy, and the Baptist church in Amesbury, and John Baker House and Queen Elizabeth Gardens in Salisbury.
Anyone who was there between 22:00 BST on 29 June and 18:30 on 30 June should continue to follow advice, including washing their clothes in a washing machine.
How nerve agents work
By Prof Alistair Hay, expert in environmental toxicology
All nerve agents poison in the same way, which is to inhibit the enzyme involved in regulating the body's messages along nerves and between nerves and muscle.
The effect is devastating, with muscles compromised and nerves linked to other organs rendered ineffective.
Glands also stop working properly and breathing becomes more difficult.
How badly affected people are varies greatly - for example, some people are able to break down the chemicals three times as fast as others.
The dose received and how long it takes to get medical treatment also influences how sick people become.