Hours after President Barack Obama and Russian President Vladimir Putin exchanged barbs during the UN General Assembly on Monday, the two leaders met for 90 minutes inside a UN Security Council consultation room.

The bilateral meeting, held in the company of ministers and advisers, including Secretary of State John Kerry, was perhaps the most eagerly anticipated conclave during this year's General Debate, which began earlier in the day. The topic of discussion was largely expected to be Syria's civil war, where Russia has recently increased its military presence, sending personnel, planes, and vehicles.

The Obama administration has insisted Syrian President Bashar al-Assad must not remain part of any political transition, while Putin says Assad should be offered support as part of efforts to dismantle the so-called Islamic State (IS). That discrepancy was on full display during the speeches the two leaders delivered earlier in the day.

After leaving the Council room, Putin bypassed an expectant group of international reporters and gave a press conference exclusively for Russian media, which was broadcast and translated live by RT, the Kremlin's English language media outlet.

According to the translation, Putin called the meeting "very constructive, practical and surprisingly frank."

"We've found a lot of common ground, but there are differences as well," he said.

Putin did not rule out the use of warplanes in Syria, but he did say, however, that Russian troops would not be deployed in fighting, saying "ground operations, involving Russian units, Russian troops — this is out of the question."

Another expected topic of discussion, which American officials insisted earlier in the week would be raised, is the conflict in Ukraine. Moscow annexed the country's Crimea region last year, and Russian soldiers have been documented inside separatist-controlled territory in eastern Ukraine. The Kremlin has insisted that its forces are not in the country.

A senior Obama administration official, briefing reporters after the meeting, described it as a "business-like back and forth."

"I think the Russians certainly understood the importance of there being a political resolution in Syria and there being a process that pursues a political resolution," said the official, who spoke on condition of anonymity. "We have a difference about what the outcome of that process would be."

The hour and a half encounter was the second of the day for Obama and Putin. Earlier, the two men sat at the same table during a luncheon hosted by UN Secretary General Ban Ki Moon. The two men clinked glasses during a toast but did not appear to speak to each other.

Asked about the incident, Putin said "this was just a protocol event nothing more."

"You journalists, you really surprise… you are very interesting people," he added.