The spokeswoman stressed that the United Kingdom refused to cooperate with Russian Federation "on fulfillment of its duties as a signatory to the Chemical Weapons Convention" and a member of the Organisation for the Prohibition of Chemical Weapons.
Sergei Lavrov said Moscow had demanded access to samples of the military-grade nerve agent.
Russian Federation denies any involvement and Foreign Minister Sergei Lavrov accused London of behaving in a "boorish" way, adding that this was partly due to the problems Britain faces over its planned exit from the European Union next year.
A Russian diplomat also claimed on Friday that the country had never had a programme called "novichok" and denied any production of the agent, despite one of the scientists who created it telling Sky News that only Russia could have been behind the attack.
"We will go after the money and actually we are going after the money", he said, adding that the National Crime Agency and Economic Crimes Unit were investigating a wide range of individuals.
In response to the attack, Britain has given 23 Russians who it said were spies working under diplomatic cover at the London embassy a week to leave.
May warned more measures could follow, noting that the US-led North Atlantic Treaty Organisation alliance and the UN Security Council had discussed the attack, while it was also expected to be on the agenda at a European Union summit next week.
Geopolitical tensions have been mounting since the poisoning of the Skripals in the English city of Salisbury on March 4, in what Western powers see as the latest sign of increasingly aggressive Russian interference in foreign countries.
South Korea says Japan's Abe expressed wish for talks with North Korea
Sweden was one of the first non-communist countries to establish diplomatic relations with North Korea in 1973. Global media have speculated that Sweden could be a potential location if the summit were to be confirmed.
Kremlin spokesman Dmitry Peskov slammed Johnson's remark in a comment to CNN. "So we will expand our "black list" with another group of Americans", Ryabkov said, according to Russia's state-run media.
"The fact that both the father and daughter came down with very similar symptoms at a similar time suggests that the contact with Novichok was fairly close for both of them", said Alastair Hay, a professor emeritus of environmental toxicology at the University of Leeds.
The leaders did not say what, if any, actions they would take if Russian Federation does not comply.
Wiltshire Police said 131 people had been identified as potentially being exposed to the nerve agent - but none has shown any symptoms.
Russian Federation described the UK's position as irresponsible and not backed up by evidence.
He also responded to Defence Secretary Gavin Williamson - who previously said Russian Federation should "go away" and "shut up" - saying: "Maybe he lacks education".
United Nations Ambassador Nikki Haley on Wednesday called on the UN Security Council to take action against Moscow for poisoning a former Russian spy in England, saying it is "a defining moment". British police said Friday that he died from compression to the neck and opened a murder investigation.