Home Secretary Amber Rudd said the policeman was not in intensive care, but was still in a serious condition following the attack.
A nerve agent, described by Ms Rudd as “very rare”, was used in an attempt on the lives Sergei Skripal, 66, and 33-year-old daughter Yulia.
Counter-terror police are working to unravel what is now feared to be a sophisticated chemical weapon plot amid heightened tensions between Britain and the Kremlin.
Defence Secretary Gavin Williamson said Russia was becoming an “ever-greater threat”, while a senior general warned the state was “capable of anything”.
Ms Rudd refused to say whether she regarded Russia as responsible, saying the investigation should be based on “facts, not rumour”.
And speaking about the officer, she told BBC Radio 4’s Today programme: “I heard this morning from the head of counter-terrorism policing that he is engaging with, talking to, people.
“But that doesn’t mean his situation isn’t serious. It remains serious. He is not in intensive care, but it’s a serious situation.”
Mr Skripal and his daughter remain critically ill.
Ms Rudd is expected to make a statement to the House of Commons about the incident shortly after noon.
Mr Williamson told ITV1’s Good Morning Britain the Kremlin had become more aggressive, including in the north Atlantic, adding: “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.”
And General Sir Chris Deverell, who oversees military intelligence as head of the Joint Forces Command, said in a speech at the defence academy in Shrivenham yesterday that Russia could seek to control systems such as traffic signals and the power grid.
In his address, he said: “They care only about what is in the interests of their elites. They don’t care about innocent people going about their lives. They are quite honestly capable of anything.”
Former British ambassador to Russia Sir Andrew Wood told the national newspaper the “assassination attempt” was more serious given a police officer was among the injured.
The former diplomat, who served in Moscow between 1995 and 2000, said: “If it is true that this is, in some fashion, the Russian state, it obviously makes it even harder to believe the Russian state is worth anything or is to be trusted.”
Assistant Commissioner Mark Rowley, the head of counter-terrorism policing, revealed Sunday’s incident in Salisbury, Wiltshire, was being treated as attempted murder and the pair had been “targeted specifically”.
He declined to specify the nerve agent or how it was administered.
He said: “Our role now of course is to establish who is behind this and why they carried out this act.”
Police have appealed for anyone who was in Salisbury city centre on Sunday to come forward to help with the “missing pieces” in the case.
Hundreds of detectives, forensic officers and analysts are working on the case, which has drawn comparisons to the poisoning of former Russian intelligence officer Alexander Litvinenko on British soil in 2006.
Nerve agents, which are chemical weapons, have been used in assassinations and attacks in war zones in recent years.
Kim Jong Un’s half-brother Kim Jong Nam was killed at an international airport in Malaysia last year in an attack using a nerve agent known as VX.
Another well-known nerve agent, sarin gas, killed more than 90 people in a rebel-held area in Khan Sheikhoun, Syria, drawing international condemnation of the Bashar Assad regime.
Access to such toxins are tightly regulated, meaning the Salisbury incident would have taken considerable planning to execute.
Russia has denied responsibility for the attack, which comes seven years after Mr Skripal was released from the country as part of a spy swap with the US.
He had been convicted in his home country in 2006 for passing state secrets to MI6.
Downing Street said Theresa May was being kept updated by officials on developments in the Salisbury case.
The Prime Minister’s official spokesman said: “It’s clear that this was an appalling and reckless crime and the public will rightly want those responsible to be identified and held to account.
“But it is important that we avoid speculation and allow police and others to rigorously establish the full facts.
“As the Home Secretary and Foreign Secretary have made clear, our response to those found to be responsible will be robust.”
The spokesman said Mrs May sent her personal thanks to police and emergency workers for their courage in responding to the incident, and also wished to thank the people of Salisbury.