An investigation has been opened into one of the cases where military officials have been suspected of talking to the press.
This comes as the New York Times and Washington Post reported on Tuesday that explosions at a Russian air base in Crimea, which are believed to have destroyed as many as 20 planes, were carried out by Ukraine.
Kyiv, however, has not confirmed or denied that it was behind the attack.
President Zelensky blasted the sharing of such high-profile information as “frankly irresponsible”.
He said in an evening address: “War is definitely not the time for vanity and loud statements.
“The fewer details you divulge about our defence plans, the better it will be for the implementation of those defence plans.
“If you want to generate loud headlines, that’s one thing – it’s frankly irresponsible.
“If you want victory for Ukraine, that is another thing, and you should be aware of your responsibility for every word you say about our state’s plans for defence or counter attacks.”
According to Deputy Defence Minister Hanna Mayler, security services have opened a probe into one of the cases of officials sharing information with newspapers.
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However, some have speculated that they were rigged and detonated remotely by Kyiv’s forces.
Mr Higgins also commented that there were “no impacts visible that look like they could be misses, so either they used very accurate weapons or they got very lucky”.
German journalist Julian Röpke shared his views on Twitter that it was “the darkest day in the history of the Russian Air Force”.