"We are not striving for any kind of leadership over Syria. Syria can have only one leader -- the Syrian people," Putin said at a Moscow investment forum, according to Reuters.
"We aim at making a contribution in the fight against terrorism, which is dangerous for the United States, for Russia and for the European countries, and for the whole world without exaggeration."
Russia surprised the world two weeks ago when it launched its first airstrikes in Syria.
The Russian airstrikes have been "reckless and indiscriminate" as well as "irresponsible," U.S. Army Col. Steve Warren, a Pentagon spokesman, said Tuesday.
On Tuesday, two mortar rounds hit near the Russian Embassy in Syria's capital during a pro-Russian rally, the Russian state-run news agency Sputnik International reported. It was not immediately clear if there were any injuries.
The Syrian state-run news agency SANA said the rally outside the embassy was a show of support by Syrians "expressing their thanks for Russia's seriousness in fighting terrorism."
Putin's comments come as the United States and Russia fuel competing sides in Syria with more firepower.
Russia has been aiding Syrian President Bashar al-Assad, whose regime faces dual threats: ISIS and rebels. Russia says it has been targeting ISIS, but many of its airstrikes have been directed at rebel-controlled areas.
The United States believes that "only a fraction" of the strikes have targeted ISIS, Warren said.
This week, the United States sent 50 tons of ammunition to rebel groups
trying to topple Assad and four decades of his family's rule.
Some observers, including Sen. John McCain, have described the ongoing escalation as a "proxy war" between the United States and Russia. The Arizona Republican sees it that way, telling CNN's Jake Tapper last week, "Of course, it is."
There's a lot at stake in Syria -- with more civilians dying every day and refugees fleeing to other countries. And there's the threat of ISIS setting up even more terror hotbeds in the volatile country.
Here's what the broader situation looks like now:
U.S. gives rebels tons of ammo
U.S. military cargo planes used an air drop of 112 pallets to deliver ammunition to rebels in northern Syria.
C-17s, accompanied by fighter escort aircraft, dropped small-arms ammunition and other items such hand grenades in Hasakah province to a coalition of rebels groups vetted by the United States, known as the Syrian Arab Coalition. Friendly forces successfully recovered all pallets, a U.S. official said.
U.S. attempt to train rebels falters
The United States launched a $500 million program to train and equip Syrian rebels -- but doesn't have much to show for it. The U.S. Defense Department announced Friday it will suspend the rebel training program
"That was a complete and total failure for a plethora of reasons," said CNN senior international correspondent Arwa Damon, who has reported from Syria.
"The U.S. was effectively dictating to these fighters, telling them they only wanted them to focus on the fight against ISIS. Whereas you speak to any Syrian, and they will tell you that they want to get rid of ISIS, yes, but they also want to be able to focus on the Syrian regime."
The low numbers are blamed on a strict vetting process that includes ensuring the fighters are committed to combat ISIS, as opposed to the Assad regime, and passing a counterintelligence screening.
Russia tries to bolster Assad with airstrikes
When Moscow began airstrikes on September 30, Russian officials said they were coordinating with Assad and targeting ISIS and other terrorists.
"Our task is to stabilize the legitimate government and to create conditions for a political compromise ... by military means, of course," Putin told the state-run Russia 24 TV.
The Russian Defense Ministry said it has targeted ISIS more than 100
times. But analysts have said Russia's focus is on Syrian rebels seeking Assad's ouster.
Even so, the Russian airstrikes have not strengthened Assad's regime, Warren said.
EU: Russian airstrikes must end
The European Union Foreign Affairs Council also isn't buying Russia's assertions that ISIS is its primary target in Syria.
"The recent Russian military attacks that go beyond Daesh and other U.N.-designated terrorist groups, as well as on the moderate opposition, are of deep concern, and must cease immediately," the group said, referring to another name for ISIS.
"The EU condemns the excessive, disproportionate and indiscriminate attacks that the Syrian regime continues to commit against its own people. The Assad regime bears the greatest responsibility for the 250,000 deaths of the conflict and the millions of displaced people."
Opposition: Syrian regime warns residents of 'crushing blows'
Assad's regime has been dropping leaflets from helicopters in Idlib province, telling residents to go to government checkpoints unarmed because their neighborhoods will be pummeled, an opposition group said.
"It is allowed for the holder of this card to cross the army's checkpoints safely, the Syrian army is going to offer the food and medical assistance for the holders of this card, cooperate with the Syrian army, leave the areas that witness clashes for your safety," the fliers said, according to the UK-based Syrian Observatory for Human Rights.
The leaflets also included warnings from the regime forces that they are going to shell the area, and that the fighters and people must leave the area and report to regime forces.
"Crushing blows are going to be carried out against this region," one flier says.
"When you get close to the Syrian army's checkpoints, be sure that you do not carry any kind of weapons, carry your personal identities and your necessary needs with you. ... When you approach to the army's checkpoint walk in the open road and lift up this card or a white cloth."
'More death and destruction'
Russia has reasons for staying allies with Syria. Its only reliable naval port on the Mediterranean Sea is there -- Tartus. The Syrian regime has purchased billions of dollars' worth of Russian weapons
Russia also doesn't believe revolutions, wars and regime change bring stability and democracy. It often points to some Arab Spring countries and the U.S.-led war in Iraq as evidence.
The United States, on the other hand, has been accused of doing too little in the first years of the civil war and is now scrambling to help rebels as they face another enemy: ISIS.
, a visiting research fellow at the Cato Institute, said more carnage will likely ensue.
"The reality is that even with the benefit of American arms, rebel forces are unlikely to be able to overcome Russian-backed regime forces," he wrote in a recent opinion piece for CNN
"As during the Cold War, U.S. and Russian arms supplies will simply fan the flames of conflict and beget more death and destruction."