Emmanuel Macron speaks with British Prime Minister Theresa May during a bilateral meeting
His vow comes after 22 people were killed and 116 injured when an ISIS suicide bomber detonated a bomb at a Ariana Grande concert in Manchester Arena on Monday night.
She said "Of course France itself knows what it is like to suffer from terrorist attacks. And these incidents show us why it is so important for us to work together in defeating terrorism."
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Macron meets May in Italy
Mourning for Manchester: The world pays tribute
Thu, May 25, 2017
Makeshift memorials and tributes to victims of the deadly attack at an Ariana Grande concert.
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Britain's Queen Elizabeth visits the Royal Manchester Children's Hospital in Manchester
Mr Macron said his country had been "shocked" by what happened in Manchester.
He said: "We will be here to co-operate and do everything we can in order to increase this co-operation at the European level, in order to do more from a bilateral point of view against terrorism.
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The leaders were speaking ahead of the annual Group of Seven (G7) meeting, which is being held in a Sicilian resort town.
France itself is on high alert following a string of terror attacks by the depraved terror group ISIS.
Italy chose to stage the summit in Sicily to draw attention to Africa, which is 140 miles (225 km) from the island at its closest point across the Mediterranean.
Mrs May is set to discuss tackling online extremism as a hot topic during the summit. She is set to leave the meeting a day earlier due to her commitments in the UK followng this week's atrocities.
May is at the G7 summit in Italy
The prime minister raised the terror threat level to critical – meaning an attack is imminet – this week.
It is the highest level Britain's terror threat level can reach.