Several NATO countries say Russian fighter jets and drones have violated their airspace in Europe over recent weeks, accusing Moscow of testing the alliance.

Asked on Tuesday whether he thought NATO states should shoot down any Russian planes that violate its airspace, Trump said: "Yes, I do."

Kremlin spokesman Dmitry Peskov on Friday denounced what he called "irresponsible statements about the need to shoot down Russian aircraft, which are, at the very least, reckless, irresponsible and carry dangerous consequences," in an interview with Russian state TV.

Peskov did not specifically refer to Trump and instead cast the calls as coming from Europe.

NATO Secretary General Mark Rutte said Thursday he supported the idea of targeting Russian jets if they violate members' airspace.

"I totally agree here with President Trump," he told Fox News, adding that NATO "will also do more, and if necessary, the ultimate to protect our people."

NATO jets intercepted three Russian MiG-31 fighters last week after they entered Estonian airspace over the Gulf of Finland.

Peskov claimed Estonia provided no evidence of the incident, and called Tallinn's rhetoric "yet another significant escalation of tensions near our border".

Denmark has several times this week been forced to close some of its airports after it said unidentified drones crossed its skies.

Earlier this month NATO scrambled jets after around 20 Russian drones flew through Polish airspace, downing at least three of them.