"We’re looking at all of it. That was an interesting situation. You saw the same tape as I saw," the president told reporters during a news conference at the White House.
Trump described Rittenhouse as acting in self-defense, saying he was "very violently attacked" by demonstrators.
"And it was something that we’re looking at right now, and it’s under investigation," Trump said. "But I guess he was in very big trouble. He probably would have been killed, but it’s under investigation."
Asked if he backs his supporters taking matters into their own hands with weapons, Trump said he'd "like to see law enforcement take care of everything."
Rittenhouse, 17, faces homicide charges after he allegedly shot and killed two people during protests Tuesday in Kenosha. The demonstrations came in response to the police shooting of Jacob Blake but have grown violent at times.
The president has faced calls to condemn Rittenhouse, who attended a Trump rally and had posted support on social media for Trump and Blue Lives Matter.
Press secretary Kayleigh McEnany was asked earlier in the day if Trump condemned Rittenhouse's actions, but she would not say.
"The president is not going to, again, weigh in on that," she said.
Separately, a man was killed in Portland, Ore., on Saturday amid clashes between right-wing groups and left-wing demonstrators. The man who died has been linked to the right-wing group Patriot Prayer. A suspect in the shooting has not been identified.
Trump on Monday more broadly declined to condemn his supporters for their actions amid unrest in Kenosha, Portland and other cities where protests against racial injustice have grown tense.
Pressed about reports that his supporters were firing paintballs at demonstrators, the president equivocated, saying paint "is a defensive mechanism. Paint is not bullets."
The New York Times tracked Rittenhouse's movements and actions on the night of the fatal shootings and found that he had been outside a car dealership carrying a rifle and told The Daily Caller he was there to defend it from unrest.
Footage later showed Rittenhouse being chased by an unidentified group of people, according to the Times. After a gunshot was fired, Rittenhouse at one point turned and shot a man in the head. He appeared to run away, stumbled a few moments later and appeared to shoot another man, the Times found, according to video footage.
Rittenhouse lives in Illinois, just over the state line from Wisconsin.
Trump is scheduled to visit Kenosha on Tuesday despite pleas from state and local officials that he stay away, warning it could foment further division and unrest.
Biden, in a statement following Trump’s news conference, blasted the president for declining to condemn Rittenhouse.
“He is too weak, too scared of the hatred he has stirred to put an end to it,” the former vice president said.
Biden argues that if Trump is unable to condemn violence regardless of political affiliation, “he is unfit to be president and his preference for more violence — not less — is clear.”