Hollande, who has said France is in a "war" against the jihadists, is continuing what could be a defining week of his three-year-old presidency.
The French president is seeking allies for his war against Isis and is hoping to persuade powers to step up their intervention following the Paris terrorist attacks.
After having met UK Prime Minister David Cameron in Paris on Monday Hollande heads to the US on Tuesday, where he will hold talks with Barack Obama in Washington.
He will also meet German Chancellor Angela Merkel and Italian Prime Minister Matteo Renzi in Paris over the next two days.
Completing a series of meetings with each of France's fellow UN Security Council members, Hollande will travel to Moscow for talks with Putin on Thursday and hold a working dinner with Chinese President Xi Jinping in Paris on Sunday.
The Security Council on Friday authorised countries to "take all necessary measures" to fight IS in a resolution that won unanimous backing in the wake of the bloodshed in Paris.
The measure drafted by France calls on all UN member states to "redouble and coordinate their efforts to prevent and suppress terrorist attacks" committed by Isis and other extremist groups linked to Al-Qaeda.
Hollande said he hoped the resolution would "help mobilise nations to eliminate Daesh", using an alternative name for Isis.
The US-led coalition has been pounding IS targets in Syria for over a year, but France joined the campaign only in September and has concentrated its air strikes on the jihadists' Syrian stronghold, Raqa.
Russia has also bombed IS targets but has attracted criticism from Western powers for bombing other rebel groups opposed to Assad, a long-time ally of Moscow.
Iran has been Assad's other main backer since an uprising broke out against his rule in 2011 and escalated into a brutal civil war.