During the brief meeting, which lasted less than five minutes, the White House said the two leaders discussed a joint statement on Syria, as well as alleged Russian meddling in the 2016 election.
The president later took to Twitter sounding off against critics who question him cozying up with the Russian leader.
"When will all the haters and fools out there realize that having a good relationship with Russia is a good thing, not a bad thing," he tweeted. "There [sic] always playing politics -- bad for our country. I want to solve North Korea, Syria, Ukraine, terrorism, and Russia can greatly help!"
He said that "progress" was being made on Syria and North Korea.
Earlier in the day, Trump spoke to reporters on Air Force One before landing in Hanoi, Vietnam on Saturday evening local time, reiterating that Putin said he did not meddle in the election.
"He said he didn't meddle," Trump told reporters. "He said he didn't meddle. I asked him again. You can only ask so many times. I just asked him again. He said he absolutely did not meddle in our election. He did not do what they are saying he did."
Asked if he believed Putin’s denial, the president didn’t directly answer but suggested he didn’t directly counter Putin’s denial.
“Well look I can’t stand there and argue with him,” Trump said. “I’d rather have him get out of Syria to be honest with you. I’d rather have him, you know, work with him on the Ukraine than standing and arguing about whether or not [Russia meddled in the election], because that whole thing was set up by the Democrats. I mean they ought to look at [former Hillary Clinton campaign chairman John] Podesta. They ought to look at all of the things they’ve done with the phony dossier."
Trump went on to say that he believes Putin "means it" when he denies meddling in the election.
"Every time he sees me he says, 'I didn't do that,' and I really believe that when he tells me that, he means it. But he says, 'I didn't do that.' I think he is very insulted by it, which is not a good thing for our country," Trump said.
He also suggested that the issue of North Korea would be a lot more easily resolved "if we had relationship with Russia. ... It would be helped a lot."
The White House confirmed that the meeting took place on Saturday after having ruled out a formal meeting would occur just a day prior, citing scheduling conflicts on both sides, after weeks of speculation on the topic.
Per a statement from Russia, the two leaders "agreed that there is no military solution to the conflict in Syria" and that a political solution must come through the Geneva process. Russia also "expressed their satisfaction with successful U.S.-Russia enhanced de-confliction efforts" and agreed to keep open lines of communication between the U.S. and Russia military.
The White House released a joint statement later, after Trump landed in Hanoi, echoing those sentiments. Trump said the two leaders "agreed very quickly" to the statement.
"The two Presidents discussed the ongoing need to reduce human suffering in Syria and called on all U.N. member states to increase their contributions to address these humanitarian needs over the coming months," the statement released by the State Department said.
"In addition, President Trump noted that he had a good meeting with President Putin," it continued. "He further noted that the successful implementation of the agreements announced today will save thousands of lives."
In addition to the one-on-one meeting, Trump and Putin were spotted shaking hands and carrying on conversation on at least three separate occasions over the course of two days at the economic summit.
Trump had previously told reporters that he expected to meet with Putin at some point during his trip.
Though the White House never confirmed that the meeting would occur, the Kremlin had previously said the “likelihood is great” for a one-on-one meeting between the two leaders and that the matter was in the works for weeks.
While the topic of Syria appears to have dominated the meeting, there are strained tensions between the two countries on a range of other issues, including the nuclear standoff with North Korea, fresh U.S. sanctions against Russia and the ongoing investigations into Russia’s meddling in the 2016 presidential election and questions of potential collusion between the Trump campaign and the Kremlin.
The two leaders previously crossed paths at the G-20 Summit in Germany this summer, where their first official bilateral meeting lasted for more than two hours. The two men also had another involved interaction at a meeting during the summit.