The United States and its European allies are expelling dozens of Russian diplomats in a co-ordinated response to the poisoning of a former Russian spy in the UK.
It is said to be the largest collective expulsion of Russian intelligence officers in history.
More than 20 countries have aligned with the UK, expelling more than 100 diplomats.
Russia vowed to retaliate to the “provocative gesture”.
Russia denies any role in the attack on Sergei Skripal and his daughter, Yulia, in Salisbury, southern England. The pair remain in a critical but stable condition in hospital.
EU leaders agreed last week it was highly likely Russia was behind the nerve-agent poisoning.
Mrs May said: “President Putin’s regime is carrying out acts of aggression against our shared values and interests within our continent and beyond.
“And as a sovereign European democracy, the United Kingdom will stand shoulder to shoulder with the EU and with Nato to face down these threats together.”
Foreign Secretary Boris Johnson also praised the “extraordinary international response” by the UK’s allies.
The Russian foreign ministry said the moves demonstrated a continuation of a “confrontational path”.
“It goes without saying that this unfriendly act by this group of countries will not go without notice and we will react to it,” its statement said.