This marked the first official face-to-face meeting between the two world leaders in the last two years.
"The relations between Russia and the US are, unfortunately, at a rather low level," President Putin said in a press conference after the meeting. "But it is not our initiative to bring the relations between Russia and the United States to such a [low] level. It's the position of our American partners."
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Both the Kremlin and the White House said beforehand that Putin and Obama planned to discuss the situations in Syria and Ukraine, among other international issues.
On Syria, the Russian president reiterated his stance that any solution to the crisis must involve Syrian President Bashar al-Assad. Putin pointed out that US President Obama and French President Francois Hollande are not Syrian citizens, and therefore should not be involved in deciding Syria's leadership.
Still, he remained hopeful that international cooperation on the crisis remains possible.
"I think there is still a way to work together on the problems we all face," President Putin said.
He also said Moscow was not ruling out the possibility of joining the airstrike campaign against the self-proclaimed Islamic State terrorist group. Putin did, however, rule out the possibility of Russian ground operations.
"We believe that the work on fighting terrorism must go hand in hand with the political process in Syria, but any participation of Russian military units in ground operations is out of the question."
Putin and Obama also discussed the creation of joint anti-terrorism mechanisms.
"We just talked about cooperation between the United States and Russia on this anti-terrorist track. We share an understanding that it is necessary to strengthen our work, at least on a bilateral basis.
"We will now jointly think about creating relevant mechanisms."
Putin also encouraged all nations to join in the work of the Baghdad Coordination Center.
On Ukraine, President Putin noted Washington's role in the ongoing crisis.
"The United States is to a known extent standing behind Kiev authorities; they are in constant contact with the Europeans," he said.
He also addressed the fact that Ukrainian President Petro Poroshenko was not present during the Russian leader's UNGA address.
"I did not notice that the Ukrainian president was not present during my speech…it's not really important to me for everyone to be present without exception, especially those that do not find it interesting."
The meeting lasted approximately one hour, due to both leaders' tight schedules.
"Events like this are helpful," Putin said. "They are very productive because there is no need to go through all the protocol and ceremony."
"This visit was very productive," he added.
The meeting followed high-profile speeches delivered by both leaders before the UNGA, as well as a state luncheon hosted by UN Secretary-General Ban Ki-moon.
Relations between Putin and Obama have been tense since the implementation of Western sanctions against Moscow last year.
"We have stated from the very beginning that the policy of sanctions and isolation in general is ineffective in the modern world, their goals are usually not achieved," Putin told reporters after the meeting.
"And with regard to a country such as Russia, this is simply impossible."