Russia did not tell South Africa that arresting President Vladimir Putin on an arrest warrant from the International Criminal Court (ICC) would mean "war", the Kremlin said on Wednesday.

Shortly after the Kremlin's comments, South Africa said that Putin would not attend a summit of the BRICS group of nations in South Africa in August "by mutual agreement."

The ICC has accused Putin and his children's commissioner Maria Lvova-Belova of the war crime of deporting children from Ukraine to Russia, something Moscow rejects as false.

A local court submission published on Tuesday had shown that South African President Cyril Ramaphosa had asked permission from the ICC not to arrest Putin in the context of the BRICS summit because to do so would amount to a declaration of war.

Speaking before South Africa said Putin would not be attending, Kremlin spokesman Dmitry Peskov told reporters that everyone understood - without having it explained to them - what an attempt to infringe on Putin's rights would mean.

"No, no such formulations were uttered, no one gave anyone to understand that," said Peskov when asked about any warning from Russia about the possibility of war if Putin was arrested.

"It is clear to everyone in this world what an attempt to infringe on the rights of the head of the Russian State means. So there is no need to explain anything to anyone here."