Mr Johnson said Russian Federation had been actively researching the use of nerve agents for use in assassinations within the past decade.
Police say they have recovered 762 exhibits and are trawling through about 4,000 hours of CCTV footage.
He also said officials from the Netherlands-based Organization for the Prohibition of Chemical Weapons would arrive Monday in Britain to take samples of the nerve agent used to poison the Skripals.
The foreign ministry said that if Russian Federation has been stockpiling nerve agents this would amount to a violation of the Chemical Weapons Convention, of which Moscow is a signatory.
Prime Minister Theresa May told MPs last week that the substance used in the attack had been identified as belonging to a group of military-grade nerve agents known as Novichok, developed by the Soviet Union.
He said it was "nonsense" to think that anyone in Russian Federation could have staged such an attack shortly before Sunday's presidential vote and before the World Cup that Russian Federation is set to host this summer.
On Saturday, the Russian foreign ministry said United Kingdom staff would be expelled from Moscow within a week, in response to Britain's decision to expel 23 Russian diplomats. "We are ready to take part in the investigation, but it's necessary that the other side shows interest in that too. But we are not taking it off the agenda, joint efforts are possible".
Johnson is expected to brief his European Union counterparts on the case at a meeting of foreign ministers and NATO Secretary General Jens Stoltenberg in Brussels on Monday.
Mr Skripal, 66, and Yulia, 33, remain in critical conditions in hospital, while Detective Sergeant Nick Bailey, who was exposed to the Novichok nerve agent while responding to the incident, is no longer considered critical.More news: Patrick's Day celebration in NYC
Putin was speaking after winning a new term in a presidential election.
"Russia had nothing to do with it", Chizhov told the BBC.
Moscow's reaction to the incident "was not the response of a country that really believes itself to be innocent", Johnson said on the BBC's The Andrew Marr Show.
Asked whether he was saying that Porton Down was responsible, Chizhov replied: "I don't know".
Johnson said Britain's National Security Council will meet later this week to decide "what further measures, if any" may be taken, and that the government may decide to target Russian wealth in Britain.
Britain and Russian Federation have each expelled 23 diplomats, broken off high-level contacts and taken other punitive steps in the escalating tit-for-tat dispute, which clouded the run-up to Sunday's presidential election in Russian Federation.
Opposition lawmakers are calling on the government to clamp down on the illicitly gained money of wealthy Russians in Britain.
Mr Yakovenko called for restraint and "cooler heads", telling the paper: "This dispute is indeed escalating dangerously and out of proportion".