In an interview with Fox Business Network anchor Maria Bartiromo, Mr Trump was asked about how the US should respond to the Russian president’s actions.
The host of Mornings with Maria asked: “I want to get your take on how Joe Biden needs to respond, to people like Vladimir Putin and [Chinese President] Xi Jinping, given the atrocious actions taken by Putin in the last seven days – possible crimes against humanity.”
She added: “Would you still afford Putin respect at this time?”
Mr Trump responded: “They have to stop killing these people. They’re killing all these people, and they have to stop it. And they have to stop it now. But they don’t respect the United States. So the United States is, I don’t know, they’re not doing anything about it.”
He added: “This is a holocaust. This is a horrible thing that’s happening, you’re witnessing. I mean, you’re seeing it on television every night.”
Despite being presented with the opportunity to condemn the Russian president, the former US president notably did not mention Mr Putin by name, nor did he respond directly to Ms Bartiromo’s question as to whether Mr Putin deserved respect.
Mr Trump has been under fire for his recent praise of Mr Putin in recent days, specifically referring to him as “savvy” and his initial moves on Ukraine as “genius”.
He also said he was playing President Joe Biden “like a drum”.
His praise for the Russian leader has stunned former aides and outraged commentators.
On Tuesday, Mr Trump lashed out at the press and much of the party he remains the de facto leader of for reporting on and criticising his decision to praise the Russian dictator.
In an emailed statement sent out by his political action committee because he is banned from most social media platforms, Mr Trump accused “the RINOs [Republicans in Name Only], the Warmongers], and the Fake News” of continuing to “blatantly lie and misrepresent my remarks on Putin”.