In a video posted online Rutte stressed that the two-week drill starting on Monday was "regular" and NATO said it is not linked directly to the Kremlin's latest actions.
"We need to do this because it helps us to make sure that our nuclear deterrent remains as credible, and as safe, and as secure, and as effective as possible," Rutte said.
"It also sends a clear signal to any potential adversary that we will and can protect and defend all allies against all threats."
NATO officials said the exercise -- which does not involve real nuclear weapons -- will involve some 70 aircraft and 2,000 personnel from 13 member states.
It will be flown out of airbases in the Netherlands, Belgium, Britain and Denmark and take place in the North Sea region.
The war game comes after a series of mysterious drones have disrupted airports and been seen at military sites in a string of NATO countries -- including Denmark.
"Drones are not a new threat to us. Drones are something we understand," said US Colonel Daniel Bunch, chief of NATO's nuclear operations.
"The more frequent incursions are obviously something we're keeping an eye on."
The exercise is the latest to be held by the alliance as the Kremlin has ramped up its nuclear rhetoric since the start of its all-out war in Ukraine in 2022.
Jim Stokes, NATO's director of nuclear policy, said allies "haven't seen any change in Russia's nuclear posture".
"We will, of course, continue to monitor on a regular basis all the Russian nuclear rhetoric, which happens quite often, and the use of dual-capable missiles in Ukraine."
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