Russia's "objectives are to go after [Isis] and to support the Government", the official said. Administration officials have expressed concern that new Russian deployments in Syria would bolster President Bashar al-Assad's fight against his opponents rather than degrade Isis (Islamic State).
In his speech, Obama took direct aim at Russia's military build-up in Syria as well its support for Ukrainian separatists, saying, "We are told that such retrenchment is required to beat back disorder, that it's the only way to stamp out terrorism, or prevent foreign meddling.
"But I stand before you today believing in my core that we, the nations of the world, cannot return to the old ways of conflict and coercion. We cannot look backward. ... And if we cannot work together more effectively, we will all suffer the consequences."
Putin, for his part, charged that attempts by Western nations to impose democracy - including in Iraq and Libya - were responsible for upheaval in the Middle East and North Africa. While people in those regions clearly wanted and deserved change, "the export of revolutions, this time so-called democratic ones", he said, had resulted in "violence and social disaster" instead of a "triumph for democracy".
Then Putin had a question. "I cannot help asking those who have forced this situation, do you realise now what you have done?" he said in remarks that never mentioned but were clearly directed at the US. "Policies based on self-conceit and belief in one's exceptionality and impunity have never been abandoned."
Beyond the barbs, the two raised the prospect of co-operating more closely on fighting Islamist terrorists and brokering a political solution in Syria, where war has raged for 4 years. Obama and Putin - who opened their first extended, formal meeting in two years with a stiff handshake before the cameras - remain divided over Assad, whom Obama wants ousted and Putin continues to back.
"The United States is prepared to work with any nation, including Russia and Iran, to resolve the conflict," Obama said in his 42-minute speech. "But we must recognise that there cannot be, after so much bloodshed, so much carnage, a return to the prewar status quo. ... And so Assad and his allies cannot simply pacify the broad majority of a population who have been brutalised by chemical weapons and indiscriminate bombing."
Putin, by contrast, insisted that "no one but Assad's forces and militias are truly fighting the Islamic State". He said it would be an "enormous mistake to refuse to co-operate with the Syrian Government and its armed forces".
Russia has directly challenged US military and diplomatic dominance in the region and the US-led coalition air campaign against Isis. Over the past month, Putin has expanded Russia's long-running provision of weapons to Assad with deployments of tanks and aircraft. Russia and Iraq announced that they would establish a rival anti-militant coalition in Baghdad to include Iran and Syria.
In his speech before UN delegates, Iranian President Hassan Rouhani echoed Putin's comments, saying that while the US was responsible for the current tumult in the Middle East, his Government was willing to help bring "democracy" to Syria.
Putin proposed creating a "broad international coalition" that he compared to the "anti-Hitler coalition" during World War II. Russia, the current chair of the UN Security Council, has called for a meeting next month to discuss how to better combat extremism. Moscow has also proposed a meeting among itself, the US and the governments of Iran, Syria, Saudi Arabia, Turkey and Egypt on co-ordination over Syria.