His inflammatory outburst comes three months before Russia hosts hundreds of thousands of foreigners for the FIFA World Cup.
Pupils were exempted classes so they could listen to the speech from a man awarded the country’s highest honour – Hero of Russia – by Putin for “courage” in defeating terrorists in Chechnya in 2000.
Fomenko used Russian slang for kill, meaning to “rub out’, famously also spoken by Putin to describe how terrorists should be extinguished.
Fomenko said in words recorded by a student that Russians encountering foreigners “must be ready to join a dispute sometimes”.
He said: “We must know at least key bits of our history in order to join a discussion.
“But the boys must also flex their muscles. When they provoke you there… in your face with a fist or a boot…you will have to tear off your clothes and, I say, to rub them all out there.
“So they know who the Russians are.”
His words were directed at Russians travelling abroad, but also appear geared to stirring hostility towards foreigners in St Petersburg, a key host city for the World Cup, which is also Putin’s birthplace.
The tourist city hosts almost three million foreigner a year, vital for its economy.
The Major General in Putin’s Interior Ministry military forces, now retired but running a union for Heroes of Russia, said his compatriots abroad face hostility both in Europe and Asia.
He urged the schoolchildren: “It is not worth crying, you must defend yourself. I don’t know about you, but I don’t like being abroad.
“I have been to Thailand, Greece [and] Turkey.
“I must tell you, I have not seen any happy faces when Russians were around.
“So don’t look at them with love either.
“Some concepts like we have here – honour and dignity – these people don’t have them.
“They have completely different needs there. So you must be alerted.
“Don’t be naïve, don’t think they think in the same way like you do.
“They think in completely different way. They have different goals.”
In 1999 Putin famously said: “We will chase terrorists everywhere. If in an airport, then in the airport. So if we find them in the (outside) toilet, excuse me, we’ll rub them out in the outhouse.”
Fomenko used the same slang word as Putin – “zamochit”, to rub out, meaning kill.
He faced a social media backlash for his comments.
“Start with yourself, General, please,” said one.
“Take this old man away from schoolchildren,” said another.
Another wrote sarcastically: “Perhaps we should offer 50% discounts on foreign tours for those who come back with the head of a local?”