Story highlights Obama said last month that "anti-American" rhetoric in Russia has increased

Putin says his job isn't to please the U.S., nor is Obama's job to please Russia

Putin accuses Kerry of lying; the State Department calls the remark "preposterous"

A U.S. diplomat says Russia is holding the U.N. security council hostage on Syria

The Cold War is over, though given the increasingly heated exchanges of late, it's hard to tell.

For decades, Moscow and Washington went at it -- diplomatically, militarily, economically, you name it -- until the 1991 fall of the Soviet Union changed the equation. Yet anyone following officials biting back-and-forth in recent days on what to do in Syria could reasonably surmise the two world powers are at it again.

What this means for what unfolds in Syria, for relations between the two nations, and for world politics generally remains to be seen. Yet a look back at comments since Vladimir Putin returned for a second stint as Russia's president, and particularly as the barbs have grown testy over the past few weeks, suggests the two sides have grown even further apart.

'I don't have a bad personal relationship with Putin'

President Barack Obama said as much in August, referring to his relationship with Russia's powerful leader.

At the same time, he acknowledged, "anti-American" rhetoric has ramped up since Putin returned to the presidency in May 2012. And, Obama added, he'd had "mixed success" trying to get "Putin to think forward, as opposed to backwards" on some issues.

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Things appeared to go differently when Dmitry Medvedev was president. (At that time, Putin had become prime minister after serving his first eight years as president.) Medvedev and Obama scored significant agreements on arms control and letting NATO troops get to Afghanistan through Russia.

Yet the atmosphere changed noticeably after Putin, a former KGB operative, resumed the top position in Russia's government. There were diplomatic flare-ups on everything from espionage to human rights to the adoption of Russian children.

One point of strain has, in many ways, the potential to have the biggest global impact: what to do about a civil war in Syria that has left more than 100,000 dead and 2 million refugees, especially given allegations from both sides about chemical weapons use.

'Obama hasn't been elected ... to be pleasant to Russia'

Putin made this comment earlier this week, before Obama and other leaders arrived in St. Petersburg, Russia, for the G20 summit.

His point, it seemed, was that the chief goal of neither he nor Obama is to ingratiate themselves to each other or please each others' citizens. Both men were elected to serve their own populaces, and if they end up throwing some elbows along the way -- well, that's how things go.

Not that the two can't make nice. Obama said their conversations are often candid and "very productive." And when they met Thursday before reporters in St. Petersburg, the two men smiled as they chatted and shook hands.

But none of that changes the fact that on the big issue of the day -- Syria -- the two are far apart.

Moscow and Washington have been at odds since 2011, when the Damascus government first cracked down on protesters. Since then, the dispute has spiraled into a full-fledged civil war pitting Syrian government forces (who, at times, have lost control over large tracts of territory) against an opposition fighting force that ranges from moderates to Islamist extremists.

Sure, both Russia -- a longtime ally of Syria and its president, Bashar al-Assad -- and the United States have been part of international efforts to forge cease-fires or a political solution. But all such attempts have failed.

'My credibility isn't on the line -- the international community's credibility is'

The issue of chemical weapons has raised the stakes, and the tensions.

In April, U.S. Defense Secretary Chuck Hagel accused al-Assad's government of being behind small-scale, but still deadly use of the nerve agent sarin. The French foreign minister made similar accusations in June.

An August 21 attack just outside Damascus put the matter front-and-center on the world stage. Within days, U.S. officials -- including Secretary of State John Kerry, who said Sunday that blood and hair samples from the scene "tested positive for signatures of sarin" gas -- blamed al-Assad's forces for an attack they estimated had killed more than 1,400 people, many of them children.

Putin and other Russian officials, however, have been skeptical of such claims from the United States, Britain and France. Russia's president said Wednesday it would be "absurd" for al-Assad -- whose government has firmly denied using chemical weapons and accused "terrorists," its blanket term for rebel fighters, of doing so -- to wage such an attack when he's gaining an upper hand.

(In fact, that same day, Russia's foreign ministry announced that its experts determined a "homemade" device that Syria's army does not possess was used in a chemical attack in March. The projectile, the ministry stated, was similar to those used in northern Syria by Bashaar Al-Nasr, an Islamist brigade that is part of the opposition Syria Liberation Front.)

Yet despite fierce resistance -- even reliable U.S. ally Britain won't join in any military intervention, following a vote by Parliament -- Obama has pressed on. Calling the Syrian attack a "challenge to the world," the 2009 Nobel Peace Prize winner has said action is necessary to enforce international chemical weapons bans.

His comment on "the international community's credibility" on Wednesday, while standing alongside Swedish Prime Minister Fredrik Reinfeldt, reflects his argument that the unfolding debate is not about whether he should live up to his 2012 comment that use of chemical weapons in Syria crosses a "red line" that must be responded to militarily.

Rather, he contended, the entire world -- not just the United States -- has an obligation to respond.

Not mentioned, but perhaps implied, is what world power more than any other has blocked international efforts to punish al-Assad's government: Russia.

'He is lying, and (he) knows he is lying'

Obama hasn't been making the case for military action alone. Kerry has been a key part of that effort not just in diplomatic circles, but also while testifying this week before Congress.

But Putin is not convinced.

The Russian president, in fact, appeared publicly perturbed by at least part of Kerry's arguments. On Wednesday, he said the top U.S. diplomat's answer to Congress regarding the presence of an al Qaeda-linked group in the Syrian opposition "is not nice."

"It was unpleasant for me to see it, because we communicate with them based on the assumption that they are decent people," Putin said of U.S. authorities. "(Kerry) knows he is lying. It's sad."

Diplomatic disagreements are part of the territory, especially when you have countries doing what they can to further their interests. But calling another country's official a liar is something else, and as a result it struck a chord in Washington.

'Such a preposterous comment'

"Sec. Kerry is, as you all know, a decorated combat veteran," State Department spokeswoman Jen Psaki said Thursday, referring to Kerry's military service in the Vietnam War while responding to a question about Putin's remark. "He's had ... more than words aimed at him.

"So he's not losing sleep after such a preposterous comment that was based on an inaccurate quote and was completely mischaracterized."

Some could see that public response from the State Department as a shot across the bow of Putin, the man who -- given his nation's geopolitical prominence and close ties with Syria -- might be seen as key to forging a long-sought diplomatic solution. It and Putin's comment hardly suggests there's much trust between the United States and Russia on Syria or whatever else.

Speaking Thursday to CNN, Russian Press Secretary Dmitry Peskov didn't say that the United States is fabricating evidence or lying, adding that he appreciates "our cooperation with American partners." And, Peskov said, he believes Russia and the United States both want peace in Syria.

"But we disagree with the (idea) that somebody in the world is trying to impose their will on another country to change the regime or government," Peskov said. "It's contrary to the international law."

'Russia continues to hold the council hostage'

Yet, some U.S. officials argue, Russia has been partly responsible for preventing international efforts to do something to halt the Syria bloodshed.

Moscow repeatedly has exercised its veto power on the U.N. Security Council to block resolutions on the crisis, many of which would have targeted its longtime ally.

Samantha Power, the U.S. ambassador to the United Nations, said Thursday, "The system has protected the prerogatives of Russia." Even after what she called "the world's largest chemical weapons attack in a quarter century," the United Nations hasn't been able to act swiftly because of Russia.

"Russia continues to hold the council hostage and shirk its international responsibilities, including as a part to the Chemical Weapons Convention," the U.S ambassador said.

Putin did say this week that he "doesn't exclude" OK'ing a U.N. measure authorizing military action if irrefutable proof is presented showing al-Assad's forces were behind the August 21 attack. Yet he didn't give any indication that he had high expectations of seeing such evidence anytime soon.

'There is no military solution'

Those are the words spoken Thursday night to G20 leaders, including Putin and Obama, by the head of the United Nations.

In prepared remarks posted on the U.N. website , and which Russia's state-run RIA Novosti news agency said he delivered, Secretary General Ban Ki-moon alluded to U.N. efforts collecting and analyzing samples from the site of the recent attack. He also spoke of the dire situation, generally, in Syria and surrounding countries that have taken on its refugees and, in some instances, been affected by spillover violence.

"It is imperative to end this war," Ban said.

Providing weapons to one side or the other isn't the answer, he argued. While not commenting specifically on Obama's call for a military strike, Ban did say the best way to resolve this issue was by talking, not fighting: "There is no military solution."

His answer as to what that solution might be involves, once again, tapping joint U.N.-Arab League envoy Lakhdar Brahimi to help "intensify our efforts towards a return to the negotiating table."

What Ban didn't say was what has changed since Brahimi and, before him, envoy Kofi Annan failed to forge a ceasefire and ultimate negotiated political deal.

Still, it seems unlikely that one development in recent days -- the acerbic spat between Russia and the United States, likely the two biggest key players to any peace deal -- will help bring the Syrian crisis any closer to a peaceful end.