London (CNN) The presidents of Russia and France spoke Thursday about strengthening their countries' shared work against terrorism, agreeing to increase the exchange of information and intelligence.

"We are all concerned by terrorism. Terrorism can strike anywhere, so we have to act," French President Francois Hollande told reporters in Moscow.

The two discussed Syria and the fight against the Islamic State. Russian President Vladimir Putin said he believes the decision about the future of Syrian President Bashar al-Assad should be decided by the people of that country.

"I believe the decision about the President of Syria should be in the hands of the Syrian people," he said, adding that Assad's army is "an ally in the fight against terrorism."

Russia is not a member of the U.S.-led global coalition against ISIS, although, on Thursday, Putin said that his country is ready to cooperate with the coalition. White House officials have repeatedly said that Assad must go if there's going to be a peace in the nation torn by war since 2011 -- a belief France shares.

Also Thursday, British Prime Minister David Cameron became the latest world leader to call for an escalation in the fight against ISIS, as Hollande continues a whirlwind week of diplomacy to build an international coalition against the terror group.

Cameron, who met with the French leader in Paris on Monday, made the case in the British Parliament for airstrikes against ISIS in Syria, arguing that an expansion of military action is needed to counter "the very direct threat that (ISIS) poses to our country and our way of life."

Britain needs "to take action now, to help protect us against the terrorism seen on the streets of Paris and elsewhere," Cameron argued.

His speech is expected to pave the way for a parliamentary vote next week on whether, in the wake of the Paris terror attacks, to expand Britain's military efforts against the Islamist militants.

The UK has been conducting strikes against ISIS on the Iraqi side of its so-called caliphate, but so far has not extended its action to the group's stronghold in Syria.

Hollande's diplomatic push

Cameron's comments came as Hollande met with Italian Prime Minister Matteo Renzi, ahead of his meeting with Putin in Moscow.

They are the latest in Hollande's busy schedule of meetings with other world leaders this week -- including Cameron, German Chancellor Angela Merkel and U.S. President Barack Obama -- as he attempts to build a broad global coalition against the Sunni extremist group, which claims to have established an Islamic caliphate over large swaths of Iraq and Syria.

Since the Paris terror attacks on November 13, Hollande has held that France is at war with the terror group and vowed to destroy it.

A French fighter jet takes off from the carrier Charles de Gaulle on Monday.

On Monday, the French military began to use the aircraft carrier Charles de Gaulle in the eastern Mediterranean to launch strikes against the group.

France and Britain are already part of a U.S.-led coalition that has been bombing ISIS targets , while Russia is conducting separate airstrikes against ISIS and other groups in coordination with the forces of Syria's President.

Any efforts to form an alliance that includes both Russia and the United States are likely to run into thorny issues -- like Assad's future role in Syria and international sanctions against Moscow for its interference in Ukraine.

Cameron: 'We cannot wait'

Outlining the case for expanded action against ISIS to British lawmakers, Cameron said the country could not afford to wait for regime change in Syria to confront the extremist threat.

Photos: The search for Paris terror suspects Photos: The search for Paris terror suspects A Belgian soldier stands guard around a security perimeter as a reported police intervention takes place around the Grand Place central square in Brussels on Sunday, November 22. Multiple raids took place throughout Brussels, according to the Belgium Federal prosecutor, and 16 people were arrested. Salah Abdeslam, a suspect in Paris terror attacks, was not among them. Hide Caption 1 of 16 Photos: The search for Paris terror suspects Belgian police officers and soldiers secure an area as a reported police intervention takes place around the Grand Place central square in Brussels on November 22. Hide Caption 2 of 16 Photos: The search for Paris terror suspects Belgian national Ahmad Dahmani, center, suspected to be involved in the November 13 Paris attacks, was arrested late Friday, November 20, in southern Antalya province, Turkey. Dahmani had been tracked by a police anti-terror unit after he arrived at the Antalya International Airport -- on a flight from Paris -- the day after the massacre. Hide Caption 3 of 16 Photos: The search for Paris terror suspects Two Syrian nationals, Ahmet Tahir, left, and Muhammed Verd, were arrested by Turkish security forces in southern Antalya province, Turkey, on November 20. They were captured, allegedly with a fake Syrian passport for Belgian national Ahmad Dahmani, suspected of location scouting for the Paris attackers. Hide Caption 4 of 16 Photos: The search for Paris terror suspects Police searched the home of Hasna Ait Boulahcen's mother in Aulnay-sous-Bois, France, on Thursday, November 19. Ait Boulahcen, 26, was killed during Wednesday's raid on an apartment in the Paris suburb of Saint-Denis, official sources in France told CNN. She did not blow herself up as was previously thought. Hide Caption 5 of 16 Photos: The search for Paris terror suspects A body is removed from an apartment that was raided by police in the Paris suburb of Saint-Denis, France, on Wednesday, November 18. French special forces were looking for those behind the November 13 terrorist attacks in Paris. The hourslong ordeal ended with at least two suspects dead and eight detained. Hide Caption 6 of 16 Photos: The search for Paris terror suspects Authorities zeroed in on the Saint-Denis building after picking up phone conversations that a relative of Abdelhamid Abaaoud, the attacks' purported ringleader, might be there. The Paris prosecutor's office later announced that Abaaoud's bullet-riddled body was found after the raid. Hide Caption 7 of 16 Photos: The search for Paris terror suspects French Interior Minister Bernard Cazeneuve visits Saint-Denis during the raid on November 18. Hide Caption 8 of 16 Photos: The search for Paris terror suspects A Renault Clio with Belgian license plates is towed by the police in Paris on Tuesday, November 17. The car is believed to have been rented by Salah Abdeslam. Authorities are looking for Abdeslam, a Belgium-born French national who is one of three brothers suspected in the terror attacks. Hide Caption 9 of 16 Photos: The search for Paris terror suspects Special forces stand guard on a roof in Molenbeek, a suburb of Brussels, Belgium, on Monday, November 16. Hide Caption 10 of 16 Photos: The search for Paris terror suspects Armed police guard a street in Brussels on November 16. Hide Caption 11 of 16 Photos: The search for Paris terror suspects Salah Abdeslam's brother Mohammed speaks to the media at his house in Molenbeek on November 16. Mohamed Abdeslam was released by police after being detained over the weekend. Hide Caption 12 of 16 Photos: The search for Paris terror suspects Special forces sit on a roof in Molenbeek as they prepare to enter a house on November 16. Hide Caption 13 of 16 Photos: The search for Paris terror suspects Armed police guard a street in Molenbeek on November 16. Hide Caption 14 of 16 Photos: The search for Paris terror suspects A man is detained by a police officer after a raid in the Mirail district of Toulouse, France, on November 16. French Prime Minister Manuel Valls said there were 150 police raids overnight in the country. Hide Caption 15 of 16 Photos: The search for Paris terror suspects Police officers overlook Paris as they patrol in front of the Sacre Coeur Basilica on November 16. Hide Caption 16 of 16

"We cannot wait for a political transition. We have to hit these militants in their heartland now," he said.

"It's the view of our military, our intelligence experts ... we should take this action as part of the coalition to help make us safer."

Assad, Syria's embattled president, could not be part of any long-term political solution for the country, he added.

Cameron said he would not call a parliamentary vote on the strikes unless he was sure of a clear majority in favor. "We will not hand a publicity coup to ISIL," he said, using another name for the extremist group.

After Cameron made his case, Labour Party leader leader Jeremy Corbyn said that he would not support airstrikes in Syria, saying that the current proposal lacked a coherent strategy.

French authorities: Attack was 'hours away'

Cameron's speech came in the wake of revelations by French authorities that another attack in Paris could have been just hours away when police closed in on the suspects last week.

The prosecutor did not elaborate on why authorities believed another plot was in the works.

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It has been more than a week since an international arrest warrant was issued for key suspect Salah Abdeslam, who remains at large.

Investigators haven't detailed what they believe his role was in the coordinated series of attacks that killed 130 people, but Molins said Abdeslam may have dropped the suicide bombers off at the Stade de France, then made his way to another Paris neighborhood. His fingerprints, Molins said, were found in a car connected with the attacks.