Obama said his talks with Putin included a direct message about cyber war, seen as a warning to Russia.
"We're moving into a new era here where a number of countries have significant capacities," Obama said at a news conference at the conclusion of the summit. "Frankly, both offensively and defensively, we have more capacity."
Obama, who had just come from a 90-minute session with Putin on the sidelines of the summit, also pointedly noted, "We've had problems with cyber intrusions from Russia and other countries in the past."
Obama said, however, that he wouldn't comment about "specific investigations that are still live and active," an apparent reference to the hack of the Democratic National Committee. While the White House has not yet named a culprit, US officials have pinned the breach on Russia.
His words on cyber weren't the only ones that pointed to areas of tension with the Russian leader.
On Syria, the topic that occupied most of their conversation, Obama said that he and Putin have had "productive conversations" about negotiating a "real cessation of hostilities" in Syria but that "gaps of trust" have prevented reaching an agreement.
"Given the gaps of trust that exist, that's a tough negotiation, and we haven't yet closed the gaps in a way where we think it would actually work," Obama said.
But he noted that he'd tasked Secretary of State John Kerry with resuming talks about a ceasefire.
Putin, Obama said, is "less colorful" than another confrontational leader, Philippine President Rodrigo Duterte, who earlier Monday warned Obama against raising his controversial record combating drug crime in an anticipated meeting.
Obama and Duterte were set to meeting in Laos this week, where Obama is traveling next to attend a meeting of Southeast Asian leaders.
Obama suggested Monday his planned meeting Duterte may not go forward.
"I always want to make sure if I'm having a meeting that it's productive and we're getting something done," Obama said during his news conference.
"If and when we have a meeting, this is something that is going to be brought up," Obama said, referring to a spate of extrajudicial killings of purported drug dealers that have transpired since Duterte took officer earlier this year.
White House officials said last week that Obama would confront Duterte about the killings.
But Duterte did not take kindly to that notion.
"I am a president of a sovereign state. And we have long ceased to be a colony. I do not have any master except the Filipino people. Nobody, but nobody. You must be respectful. Don't ask just throwaway questions and statements," Duterte told reporters in Davao City before he left for the Vientiane, capital of Laos, where the ASEAN summit is taking place.
"Who is he (Obama) to confront me?" Duterte scoffed in a speech Monday. "Son of a b****, I'll cuss you in that forum."
The news conference wrapped up a three-day stay in Hangzhou, in which Obama also met with the leaders of China, the United Kingdom and Turkey -- all countries with complicated but integral relationships to the US.
It was one of Obama's final chances to engage in face-to-face diplomacy with his counterparts before a new president is elected in November. Many leaders are already looking ahead to January, when either Hillary Clinton or Donald Trump assumes the business of state.
During his news conference, Obama faced questions about both candidates' opposition to the Trans-Pacific Partnership trade deal, a centerpiece of his Asia policy, which he's urgently trying to promote on his final trip to the continent as its fate hangs in the balance.
"I've yet to hear a persuasive argument from the left or the right" against the TPP, Obama argued during the news conference.
"Back home, we'll have to cut through the noise once the election season is over," he said when probed about the prospects of passing the deal this year through a Congress largely antagonistic to the pact.
Obama also addressed a domestic controversy over NFL quarterback Colin Kaepernick's refusal to stand during the playing of the national anthem in protest of the treatment of minorities in the United States.
"He's exercising his constitutional right to make a statement," Obama said. "I think he cares about some real, legitimate issues that need to be talked about and, if nothing else, what he's doing has generated more conversation around some topics that need to be talked about."
Obama departs China Monday for Laos, where his Pacific trade plan will take center stage. He'll be the first sitting US president to visit the small Southeast Asian nation.