Russia, which denies any involvement in the attack, called the measures announced by May "unacceptable, unjustified and shortsighted" and warned Britain to expect retaliation.
The Russian statement said the government could take further measures if Britain takes any more "unfriendly" moves toward Russia.
The updates of their medical conditions come as the Foreign Secretary Boris Johnson said it was "overwhelmingly likely" that Vladamir Putin directed the use of the nerve agent on Britain's streets.
"Twenty-three diplomatic staff at the British embassy in Moscow are declared persona non grata and to be expelled within a week", the foreign ministry said in a statement after summoning the British ambassador Laurie Bristow.
Responding to the accusations and expulsions by Britain, Kremlin spokesman Dmitry Peskov called Johnson's remarks "shocking and unforgivable".
The UK government was backed this week by allies France, Germany and the United States in its assessment that there was "no plausible alternative explanation" than that Russian Federation was responsible for the nerve agent attack.
They were found unconscious on a bench in Salisbury, Wiltshire on 4 March.
Britain is expelling 23 Russian diplomats and taking other steps against Russian interests as the two nations' relations sink to a post-Cold War low.
United Kingdom officials believe the Skripals were exposed to a nerve agent known as Novichok that was developed in Russian Federation.
"The onus remains on the Russian state to account for their actions and to comply with their worldwide obligations", the British Foreign Office said Saturday.More news: 'BJP will be reduced to 110 seats in 2019' - Shiv Sena
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And she also warned more measures could follow, noting that the US-led North Atlantic Treaty Organisation alliance and the UN Security Council had discussed the attack.
Russian Federation denied involvement in his death. Lavrov said that Russian Federation "has stopped paying attention" to allegations against them, suggesting it is a violation of worldwide law that May is now refusing to work with Russian Federation.
"That's making a lot of people anxious, more worried than it was before", said Russian exile and former cell phone magnate Yevgeny Chichvarkin. This comes as United Kingdom police launch a murder investigation into the death of an exiled Russian businessman.
President Donald Trump joined British Prime Minister Theresa May and the leaders of Germany and France on Thursday to issue a joint statement pinning the blame for the attack squarely on the Russian government.
Speaking on Russia-24 television, Zakharova on Saturday linked Britain's angry reaction to the war in Syria.
In a dramatic twist Friday, London's Metropolitan Police said that the death of Russian businessman Nikolai Glushkov, who was found dead Monday in his London home, was now being treated as murder.
The murder is not believed to be linked to the attack on Skripal and his daughter.
The paper said investigators were looking into whether an item of clothing, cosmetics or a gift that was opened in Sergei Skripal's house in Salisbury may have been impregnated with the poison.
Skripal, who is a retired Russian military intelligence officer, was jailed for 13 years by Russia in 2006 for spying for Britain.
According to British experts, the toxin used in the attack was part of a group of nerve agents known as Novichok, which was developed in the former Soviet Union.