Mr Hollande has met with several world leaders in an effort to build a stronger front against the group.
It comes two weeks after the deadly attacks on Paris.
French president Francois Hollande has ended his whirlwind diplomatic tour in Russia, holding talks with President Vladimir Putin at the Kremlin.
Since the start of the week, he has met with various world leaders to try to gain support for a stronger, more united offensive to bring down IS, also known as Daesh.
It follows a series of attacks on Paris on November the 13th in which 130 people were killed and more than 300 injured.
After a working dinner between the two presidents, Mr Hollande seems confident.
"I am convinced that Russia can play a major and leading role in this process, which I have just described. I pointed out to President Putin that France would like to work with Russia for a clear objective, a simple objective: fighting Daesh and terrorist groups, and them and them alone."
Russia has its own motivation to work with the global community after IS claimed responsibility for downing a Russian passenger plane over Egypt in October.
But Turkey's shooting down of a Russian warplane on the border with Syria has strained relations, as has Russia's clash with the West over Syrian president Bashar al-Assad's role.
President Putin made it clear his position on the Syrian leader has not changed, while emphasising he agreed with Mr Hollande to only attack IS fighters.
"But we're also supporting the army of President Assad. We agreed that this is an important part of our agreement with President Hollande, and we will continue to exchange the information on which territories are occupied by healthy parts of the opposition and not terrorists, and we will refrain from attacking them."
The two men will meet again at the United Nations climate conference in Paris on Monday.
In Britain, Prime Minister David Cameron has advocated Britain joining airstrikes against IS, or ISIL, targets, saying the nation needs to ensure its own safety.
"The reason for acting is the very direct threat that ISIL poses to our country and to our way of life. ISIL has attacked Ankara, Beirut and, of course, Paris, as well as the likely blowing up of a Russian plane with 224 people on board. They've already taken the lives of British hostages and inspired the worst terrorist attack against British people since 7/7 (July 7, 2005) on the beaches of Tunisia. And, crucially, they have repeatedly tried to attack us right here in Britain. So I'm in no doubt that it is in our national interest for action to be taken to stop them. And stopping them means taking action in Syria, because it is Raqqa that is their headquarters."
Two years ago, Mr Cameron lost a parliamentary vote to launch airstrikes against the Syrian government.
A new vote may be held next week.
Britain has largely been opposed to entering another conflict in the Middle East, but the recent major attacks have reignited the debate.
Some politicians, such as Labour leader Jeremy Corbyn, remain vehemently opposed.
"In the light of the record of Western military intervention in recent years, including Iraq, Afghanistan and Libya, does the Prime Minister accept the UK bombing of Syria could risk more of what President Obama called 'unintended consequences'?"
Meanwhile, Germany has thrown its support behind France, committing jets, refuelling aircraft and a frigate.
The German parliament must first approve the measures, promised by Chancellor Angela Merkel after meeting with Mr Hollande.
Germany has ruled out conducting airstrikes in Syria.
Defence Minister Ursula von der Leyen says Germany will not hesitate to help an ally as close as France.
"France has been rocked to the core by the terrible attacks by IS. But we all know that this inhumane rage can also hit us and other societies at any time. France has asked us for help, and today we discussed how we can accommodate this request for help. What we can do above all is in three parts: protection, the important task of reconnaissance and logistics."
But Francois Hollande received cooler receptions in both Italy and the United States earlier.
US president Barack Obama has talked of intensifying US efforts, but not militarily.
"Today, President Hollande and I agreed that our nations must do even more together. US assistance has supported recent French strikes in Syria, and we're going to keep stepping up that coordination. And as we saw with the attack in Mali, the terrorist threat goes beyond ISIL. The United States will continue to quickly share threat information with France, and, in the wake of Paris and with the threats in Belgium, there's also a growing recognition among European nations that they need to ramp up additional efforts to prevent the flow of foreign terrorist fighters."
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