The two presidential candidates argued over Russia's invasion of Ukraine at the National Constitution Center in Philadelphia on Tuesday night.
Harris told Trump that Putin "would eat you for lunch." She also said that the Russian leader would be "sitting in Kyiv right now" if Trump were president.
Trump wouldn't say whether he wanted Ukraine to win the war, instead claiming he could help the two nations facilitate a deal.
"I want the war to stop," Trump said. "I want to save lives."
"I will get it settled before I even become president," he added, echoing a previous remark that he could end the war in 24 hours.
"I believe the reason that Donald Trump says that this war would be over within 24 hours is cause he would just give it up," Harris said.
"And that's not who we are as Americans," she said.
Putin's spokesperson, Dmitry Peskov, told reporters that the Kremlin hadn't followed the debate directly but was aware of news reports mentioning the Russian president's name.
"Of course, we noticed that both candidates mentioned our president, mentioned our country. Of course, the position is quite clear — the US as a whole, no matter which party the candidates are from, maintains a negative attitude, an unfriendly attitude towards our country," he said in a statement cited by Reuters .
He continued: "Putin's name is used as one of the instruments in the domestic political struggle in the US. We really, really don't like it, and we hope that they will leave our president's name alone."
The comments were starkly different in tone from Putin's joking expression of support for Harris when asked about the US election during an economic forum last week.
The Russian president said that since Biden had asked his supporters to back Harris, "we will do the same, we will support her," Reuters reported .
"She laughs so expressively and infectiously that it means that everything is fine with her," he said, adding that maybe it would mean she would prevent further sanctions against Russia.
The Kremlin did not immediately respond to a request for comment.
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