President Barack Obama has reportedly vowed not to let the conflict in Syria become a US-Russia proxy war, saying that would be a bad strategy for the United States.

The US President has labelled Russia's military actions in Syria as self-defeating. He pointed out though that the situation in Syria is not some sort of a contest between the two superpowers.

"This is not some superpower chessboard contest,'' the US President said, according to USA Today. "And anybody who frames it in that way isn't playing very close attention to what's been happening on the chess board."

Obama's view is the opposite of Sen. John McCain's assessment that the US is now engaged in a proxy war with Russia in Syria as a result of "an abdication of American leadership'' by the White House.

McCain said Russian President Vladimir Putin is "treating the United States with disdain and contempt" over Syria by carrying out airstrikes and "inserting himself into the Middle East in a way that Russia has not been since Anwar Sadat threw them out in 1973.''

"He is now dictating the pace of events in Syria, which is of course an abdication of American leadership,'' McCain, who is also chairman of the Senate armed forces committee, told CNN.

"... and of course they're hitting the Free Syrian Army enclaves and places which have had some success. This is the CIA-run operations, and they want to take them out," he added.

McCain said Putin's strategy was to "provide us with a choice between ISIS and Bashar Assad.''

The senator also noted that as a result of failed White House policy, the world is now experiencing a flood of refugees. "It was a year ago the president said our goal was to degrade and destroy ISIS. We've made no progress there...''

Russia's dramatic entry into the Syrian civil war, after a year of airstrikes by the US and its coalition partners, has raised the spectre of dangerous confrontations in the skies over Syria.

Last week, Obama reportedly tried to forge a consensus with Putin on Syria but repeatedly downplayed the importance of the airstrikes by Russia.

"Mr. Putin had to go into Syria, not out of strength but out of weakness because his client Mr. Assad was crumbling and it was insufficient for him simply to send them arms and money. Now, he's got to put in his own planes and his own pilots.''

Obama also said that while he admits that his own "train-and-equip'' policy of arming moderate opposition forces in Syria has not worked well, Russia should not drive folks underground, or create a situation in which they are decapacitated as this would only strengthen the ISIL.

Obama also rejected calls from Republican critics and even Democrat Hillary Clinton to enforce a no-fly zone over Syria, USA Today said.