His comments came after US officials said this week that there is strong evidence that the Democratic National Committee data breach was carried out by hackers working on behalf of Russian intelligence.
"Anything's possible," Obama responded when asked during an interview whether Russians could be working to influence the contest between Republican nominee Trump and Democratic rival Hillary Clinton.
"Donald Trump has repeatedly expressed admiration for Vladimir Putin," Obama said during the sit-down with NBC News that aired Tuesday. "And I think that Trump's gotten pretty favorable coverage back in Russia."
Democrats have been alleging that Putin is seeking to alter the White House race after WikiLeaks released damaging emails from the organization's staff following the hack.
On Wednesday the Kremlin denied allegations that Russia was involved with the DNC hack. Talking to journalists in Moscow, Kremlin press spokesman Dmitry Peskov said, "The only thing I can tell -- President Putin said numerous times that Russia has never interfered and doesn't interfere in domestic affairs of other countries, especially in electing campaigns. Moscow carefully avoids any actions or words that might be seen as interference in an electoral process."
He also warned that "We denied it numerous times as well. Talking about suspicions in regards to the country -- you need to be at least very precise and concrete. Hypothetical reasoning in this case does not indicate a constructive attitude."
The DNC breach occurred around the same time as breaches of US government systems at the State Department and the White House. Analysts from the NSA and FBI investigators found signatures in those breaches that led them to other intrusions outside the government, including at the DNC.
Investigators have tracked the IP addresses and other data from the DNC hack and found they matched attacks around the same time at other federal agencies.
Evidence points to at least one group of hackers that is familiar to US counterintelligence, officials said. This same group was involved in hacking into non-classified systems email systems at State, White House and other federal agencies. Investigators believe Russian intelligence is behind a wave of cyber attacks on political organizations and even think tanks in Washington.
The timing of the release has raised suspicions among US intelligence that this was aimed at influencing the US election. Though WikiLeaks has denied the Russian government provided the documents to the group but will not say where they came from.
In the NBC interview, Obama said, "What we do know ... is that the Russians hack our systems. Not just government systems, but private systems."
The President's comment was the furthest the US government has gone in publicly blaming Russia for carrying out cyber attacks on the US.
In a bid to discourage cyber attacks by foreign governments, the administration in recent years has pursued a "name and shame" policy, publicly attributing computer intrusions to government entities in China, North Korea and Iran. But not Russia.
White House homeland security adviser Lisa Monaco, appearing Tuesday at a cyber-security conference hosted by the FBI and Fordham University in New York, said there wasn't a reluctance to name Russia. Determining attribution takes investigative work, which is ongoing, she said.
Though the Obama administration has declined to publicly label Russia the perpetrator in the DNC hack, Secretary of State John Kerry said he had raised the issue with Russian Foreign Minister Sergey Lavrov after WikiLeaks posted the DNC emails.
Earlier Tuesday, Clinton's campaign manager suggested Russia was attempting to damage Democrats as they begin their nominating convention in Philadelphia.
"I don't think it's coincidental that these emails were released on the eve of our convention here, and I think that's disturbing," Robby Mook said.
Trump has expressed admiration for Putin as a leader, even as the Russian president remains deeply at odds with the US following his incursion into Ukraine and his support for Syrian President Bashar al-Assad, whom the US has called on to leave office as a bloody civil war rages in his country.
Meanwhile, the Republican's skepticism of NATO -- intended as a line of defense against further Russian aggression in Europe -- is said to appeal to Putin. Clinton has vowed a tough approach to territorial disputes involving Russia.
At the Democratic convention Tuesday night, former Secretary of State Madeleine Albright argued that, "The truth is that a Trump victory in November would be a gift to Vladimir Putin."
Trump campaign chairman Paul Manafort told CNN that those suggestions were "crazy."
Trump himself tweeted a similar sentiment on Tuesday.
"In order to try and deflect the horror and stupidity of the Wikileakes disaster, the Dems said maybe it is Russia dealing with Trump. Crazy!" he wrote. "For the record, I have ZERO investments in Russia."