“Where we are now after this Ukraine success in the north is not that point,” he said. “But it is a lot closer to it than we’ve been before.”
Mr Bolton was then-President Donald Trump’s national security adviser between 2018 and 2019.
He said he has “always” thought that Mr Putin would avoid the use of nuclear weapons unless the Ukrainians became likely to cross the Russian border.
“The potential risk of the use of a nuclear weapon is not so much to change the battlefield but to strengthen Putin’s position at home,” he said.
Ukrainian forces began a counteroffensive last week in the north following a disinformation campaign to make the Russians believe an attack in the south was coming.
Mr Bolton said he considers Mr Putin’s position to be “endangered” and that he’s in “more trouble now than he’s been since the invasion” that began on 24 February.
“We need to think about how to take advantage of that,” Mr Bolton added.
Mr Bolton, who also served as United Nations ambassador under former president George W Bush, said that there’s “no chance” that Russia would surrender following the Ukrainian counteroffensive.
“That would be a signal of weakness,” he added. “This defeat is significant enough that it will have political effects.”
Mr Bolton said the Ukrainians deserve “great credit” for their strong efforts in response to the invasion.
“Just when you think the Russian military can’t perform any worse, they surprise you and perform worse,” he said.
Ukrainian President Volodymyr Zelensky said on Monday that they have taken back 6,000 square kilometres of land from Russia.
“From the beginning of September until today, our warriors have already liberated more than 6,000 square kilometres of the territory of Ukraine – in the east and south,” he said in a speech. “The movement of our troops continues.”
He accused Russia of being “the biggest source of terror in the world”.
“Why can it wage the war so cruelly and cynically?” Mr Zelensky asked. “There is only one reason, insufficient pressure on Russia. The response to the terror of this state is insufficient.”
Ramzan Kadyrov, the autocratic leader of Chechnya put in place by the Kremlin, criticised the Russian war machine in an audio message on his Telegram account on Sunday.
“If today or tomorrow no changes in strategy are made, I will be forced to speak with the leadership of the defence ministry and the leadership of the country to explain the real situation on the ground to them. It’s a very interesting situation. It’s astounding, I would say,” he said, according to The Guardian.