"The President has made a decision to cancel this visit (to Paris)," Kremlin spokesman Dmitry Peskov told Russian state-run news agency TASS.
Putin was scheduled to attend events linked to the opening of a Russian religious and cultural center, but the trip was canceled because the events "fell out of the program."
But a French government official told CNN that Putin canceled because he did not agree with Hollande's request that the meeting be dedicated to Syria.
Hollande had earlier suggested to French TV station TF1
that he was mulling whether to cancel the meeting with Putin, saying that those behind the bombardment of Aleppo -- alluding to Syria and Russia -- had committed "war crimes" in the Syrian city
and should be held accountable at the International Criminal Court.
Putin was scheduled to visit Paris October 19.
Debating whether to meet Putin, Hollande told TF1: "I have asked myself that question: Is it useful? Is it necessary? Could we do something that pushes him as well and stop what they're doing with the Syrian regime -- that is to say the help they are providing to the Syrian regime, which sends bombs to the population of Aleppo?
"If I receive him, I would tell him that it is unacceptable, that it is bad even for the image of Russia. What I tell them, is that these populations are populations that are today victims of war crimes and those who commit those acts will have to pay for their responsibility in front of the International Criminal Court."
Russia has carried out airstrikes in Syria since September 2015 in coordination with President Bashar al-Assad's regime. Moscow says it is targeting militant groups, but the United States is arming some of those same groups to fight the Assad government, essentially pitting the Cold War enemies against each other.
Fresh strikes on Aleppo
After six days of relative calm in Aleppo, renewed airstrikes on rebel-held areas killed at least 41 people on Tuesday, according to activists and residents.
Around 20 airstrikes, including cluster munitions and bunker-busting bombs, hit seven neighborhoods in the besieged eastern parts of the city, according to an activist with the Aleppo Media Center (AMC).
The heaviest strikes occurred in the neighborhood of Bustan al-Qasr, with several missiles landing near a market and a school, according to residents and activists.
Stranglehold in Aleppo
Russia's UN veto on the Aleppo resolution Saturday had been widely expected.
Hollande's war crimes comments echo those of US Secretary of State John Kerry, who said airstrikes by Syrian forces with Russian support should be investigated.
"Russia and the regime owe the world more than an explanation about why they keep hitting hospitals and medical facilities, and children and women. These are acts that beg for an appropriate investigation of war crimes," Kerry said.
In July, regime forces encircled rebel-held parts of Aleppo, mostly in the city's east, creating a stranglehold that cut the population off from basic food, water, medical and fuel supplies.
Aid agencies have struggled to make deliveries into the besieged city. An aid convoy last month was attacked when it was finally able to enter after a days-long ceasefire.
The Syrian regime has pounded rebel-held Aleppo with airstrikes since July, but it scaled back last week as it began a ground offensive to take back parts of the city.
It has been accused of using chemical weapons, such as chlorine gas, on the population there, an allegation that Syria and Russia deny.
Rebels have held parts of eastern Aleppo since 2012.
So what's behind the apparent snub?
Putin survives on his popularity, which is built on his image as a strongman, and his image would be damaged if he went to Paris just as the French were essentially calling on Russia to be tried for war crimes, explained CNN Senior International Correspondent Nic Robertson.
In his own country, a French visit would look weak, and that's the most important thing to him, Robertson added.
France's accusations of war crimes appear to be part of a growing trend. The United States has also accused Russia of war crimes as it has tried every other form of diplomacy.
The world has expected Russia to put pressure on Assad -- and it's believed that Moscow hasn't acted in good faith, so the world now needs to put pressure on Russia, Robertson said.
And one way to do that is by publicly pointing out to Russia that at some point in the future, it could be held accountable for war crimes -- killing civilians, breaking the conventions of war and international humanitarian conventions, like targeting hospitals.
While Russia has strongly denied war crimes allegations, Robertson explained, Western powers see legitimate grounds to call for investigations, and for these investigations to focus on Russia.
Putin's decision to cancel his trip also shows a growing gap between Russia and France, and Russia with Europe at large.
The EU is looking at developing a common defense policy, which at the moment is in effect NATO.
Russia and Putin have been extremely angered over the past decade, at least whenever NATO bolsters its forces along its eastern borders, while NATO sees Russia as developing hardened and more secure defense facilities all the way from Kaliningrad in the north now to Syria, with their announcement of a permanent military base there
There are also implications for Ukraine. The Normandy 4 -- Ukraine, Russia, Germany and France -- have been the principle states in addressing the Ukraine conflict. They brought about the Minsk Agreement that was supposed to solidify a ceasefire and bring back all of Ukraine's borders under Kiev's control.
That hasn't happened, Robertson said, so normally you would expect more dialogue to be going forward with this group. However, this incident with France and Russia makes that less likely and makes instability in Ukraine more likely. This also means Europe's Ukraine-related sanctions on Russia are unlikely to be lifted anytime soon.