Vladimir Putin has accused the UK and US of "provocation" following the incident involving HMS Defender.
The Royal Navy warship was shadowed by Russian vessels and buzzed by jets as it sailed through the disputed waters around Crimea last week.
The Russian president claimed there was US involvement in the operation, with an American plane sent to monitor Moscow's response.
Moscow claimed that warning shots were fired by Russian vessels at the Type 45 destroyer as it passed through the contested part of the Black Sea on 23 June – an assertion dismissed by the UK Government, which said only that a routine "gunnery exercise" took place.
Russia also threatened to "drop bombs... right on target" if Royal Navy vessels sail again through waters around Crimea.
During a marathon live call-in show on Russian television, Mr Putin said "I don't think we were on the brink of World War Three" but the incident "was a provocation".
According to a translation of his comments on the Russian state-backed RT channel, Mr Putin said: "What were they trying to tell us, what goals were they trying to achieve?
"It was a complex provocation organised by the US and the British because a warship entered our waters during the day and then at 5pm an American warplane took off from somewhere in Greece."
Watch: Russia released footage of the alleged 'border violation'.
The incident happened off the Crimean peninsula, which Russia annexed in 2014 but the UK still recognises as part of Ukraine.
Mr Putin said HMS Defender "came into our waters and they looked at how we were going to respond" then "the plane was looking at how we were going to respond".
It comes as the Netherlands on Tuesday afternoon accused "armed Russian aircraft" of causing a "dangerous situation" in the Black Sea last Thursday – the day after the incident with HMS Defender.
In a tweet, the Dutch defence ministry said jets "repeatedly flew dangerously low over and close" to HNLMS Evertsen, and "carried out mock attacks" whilst in international waters.
HNLMS Evertsen has been part of the UK's maiden operational Carrier Strike Group deployment, of which HMS Defender is also a part.
The incident involving HMS Defender came a week after Mr Putin's meeting with US President Joe Biden in Geneva and the Russian president appeared to suggest there could be a link to the incident off the Crimean peninsula.
Prime Minister Boris Johnson backed the actions taken by HMS Defender, saying it was "wholly appropriate to use international waters".
"We don't recognise the Russian annexation of Crimea, this is part of a sovereign Ukrainian territory, it was entirely right that we should indicate the law and pursue freedom of navigation in the way that we did, take the shortest route between two points, and that's what we did."
Dramatic eyewitness accounts revealed the Type 45 destroyer was buzzed by Russian military jets and the sound of naval gunfire could be heard as it sailed from Odessa in Ukraine to Georgia on Wednesday.
Defence Secretary Ben Wallace said that 10 minutes after entering the traffic separation scheme shipping lane inside Ukrainian territorial waters, a Russian coastguard vessel "warned that Russian units would shortly commence a live-fire gunnery exercise".
HMS Defender was overflown by Russian combat aircraft at varying heights, the lowest of which was approximately 500 feet, with some of the manoeuvres "neither safe nor professional", Mr Wallace told MPs.
Cover image: Library photo of HMS Defender (Picture: Royal Navy).