The Times reported that he said: "You have tanks and armour rolling across the Ukrainian border, and you have an Estonian border guard being captured and not yet still returned.
"It is very important when Russians looks at countries like Estonia or Latvia or Poland that they don't just see Estonian, Latvian and Polish soldiers – they see French, German, British soldiers too," he said.
There is even an Estonian vodka called Russian Billionaire Elite Club.
The head of the Estonian internal security service, Arnold Sinisalu, said his officers were under strict orders never to cross the border.
The evening, which includes the world premiere of LamenTate, a composition by Estonian composer Arvo Part, also inspired by Marsyas, was originally planned last summer as Kapoor completed his huge sculpture, but has been shaped against the gathering clouds of war.
Estonian security sources confirmed that all the items were Kohver's but said it was entirely routine for him to be carrying them.
He had armed backup in the form of Estonian security officers nearby but they were unable to react in time because of the use of flash grenades and because their communications were jammed.
Russia's FSB security service said in a statement it had detained Kohver in north-western Russia, close to the Estonian border, on Friday as he attempted to carry out an "undercover operation".
"I see that he's bored in the [parliament], plus he's now been seriously wounded in battle, and I would love to create a volunteer defence union of Ukraine with Dmytro Yarosh like in the Estonian, Finnish and Swiss systems," he said.
The Estonian intelligence official seized by Russia thought he was going to meet an informant in a secluded spot on the border as part of an organised crime investigation but instead walked into an FSB trap, according to Estonian security sources.
In September, Russian operatives reportedly jammed communications and threw smoke grenades in order to abduct an Estonian special services agent from a border post that Estonia said was located in its territory.
