He said such an action from Europe and the US would force the Russian government to act and any countries hosting US missiles would be at risk of Russian strikes.
The Russian President said his response would be “very fast and effective”.
US President Donald Trump at the weekend announced his intention to withdraw from the Intermediate-Range Nuclear Forces Treaty (INF), signed in 1987 between the US and the Soviet Union.
The agreement halts Washington from creating further nuclear weapons.
At a rally in Nevada on Saturday, Trump said: “Russia has violated the agreement. They have been violating it for many years.
“And we’re not going to let them violate a nuclear agreement and go out and do weapons and we’re not allowed to.”
Trump warned that the US would begin developing new weapons unless Russia and China agree not to possess or produce more.
China is not officially part of the pact.
Putin, who claims the US violated the treaty, responded that if the US were to do this it “would be a very dangerous step”.
He added: “There would be nothing left except an arms race.”
At the press conference following a meeting with the Italian Prime Minister Giuseppe Conte yesterday, Putin addressed the issue again.
He said: “If the US do end up pulling out of the INF treaty, then the most important question is what will they do with the missiles that will reappear again.
“If they are supplied to Europe, then of course we will have to respond in kind and the European countries that agree to this – if things come to this – should understand that they will be subjecting their own territory to the threat of a possible retaliatory strike.”
According to reports, Putin hopes to discuss the INF pact with Trump on November 11, when the two leaders will be at an event marking the 100-year anniversary of the end of the First World War.
NATO has said it is unlikely to deploy more nuclear weapons to Europe should the arms treaty between Washington and Moscow collapse.
However, NATO Secretary-General Jens Stoltenberg agreed that Russia had probably violated the deal.
Trump and Putin’s comments on nuclear weapons come as NATO begins its largest military exercise since 2002, which is being held in Norway and will involve over 30 countries.