Clinton said Trump had refused to condemn Putin and Russia for recent cyber attacks on the United States.
Clinton said Trump is Russian president's puppet, with Trump charging Putin had repeatedly outsmarted Clinton.
In a third and final U.S. presidential debate that focused more on substantive policy issues than the personal attacks of the first two debates, Clinton said Trump had refused to condemn Putin and Russia for recent cyber attacks.
"He'd rather believe Vladimir Putin than the military and civilian intelligence officials that are sworn to protect us," Clinton said.
U.S. intelligence agencies and the Department of Homeland Security have said the Russian leadership was responsible for recent cyber attacks on the Democratic National Committee and the leaking of stolen emails.
Trump rejected the idea that he was close with Putin, but suggested he would have a better relationship with Russia's leader than Clinton.
"He said nice things about me," Trump said. "He has no respect for her, he has no respect for our president and I'll tell you what, we're in very serious trouble."
Clinton responded: "Well that's because he'd rather have a puppet as president of the United States."
"No, you're the puppet," Trump retorted. "Putin has outsmarted her and Obama every single step of the way," he said in a reference to U.S. President Barack Obama, a Democrat like Clinton.
Clinton also said Trump had been "cavalier" about nuclear weapons and should not be trusted with the nuclear codes.
The two presidential rivals had tough but issues-based exchanges on abortion, gun rights and immigration during the 90-minute showdown.
Trump seeks to reverse his fading momentum in a U.S. election that opinion polls show is tilting away from him. The New York businessman, 70, has been damaged by several accusations he groped women - which he denies - and concerns about his claims the election will be rigged against him.