Earlier this year, Trump made an off-the-cuff comment about Russia finding missing emails from Clinton's controversial private server. Some reports have suggested Russia was behind the hacking of the Democratic National Committee.
"I was so shocked when Donald publicly invited [Vladimir] Putin to hack into Americans. That is just unacceptable," she said at the first presidential debate at Hofstra University.
Trump said he didn't think "anybody knows it was Russia that broke into the DNC."
"It could be Russia but it could also be China. It could be lots of other people. It also could be somebody sitting on their bed that weighs 400 pounds," he said.
Clinton called Trump "very praiseworthy" of the Russian President Putin, who has consolidated power in Russia under his personal control.
Markets seemed to react to Clinton making headway against her GOP rival as Monday night's debate progressed.
U.S. stock index futures erased losses to trade higher during the debate, and the Mexican peso reversed losses to trade more than 1 percent stronger against the U.S. dollar.