"She's accusing everyone of being a Russian agent," Trump told reporters. "She's not a Russian agent. These people are sick. There’s something wrong with them."
Clinton strongly suggested Gabbard was "the favorite of the Russians" during an interview on a podcast with former Obama adviser David Plouffe last week.
She went on to say that she wasn't "making any predictions, but [thinks Russians] have got their eye on somebody who is currently in the Democratic primary and are grooming her to be the third-party candidate."
Gabbard responded on Twitter, saying the former secretary of state and 2016 Democratic presidential nominee was the "queen of warmongers, embodiment of corruption, and personification of the rot that has sickened the Democratic Party for so long."
On Monday, Trump said Clinton and Democrats claimed everyone opposed to them were Russian agents. He said Clinton's attack may boost Gabbard's and his political chances.
The Associated Press contributed to this report.