"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.
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.
"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.
Suspected ringleader Abdelhamid Abaaoud
and another man were planning a suicide attack on the Paris financial district of La Defense on November 18 or 19, Paris prosecutor Francois Molins said Tuesday. But both men were killed during a raid in Saint-Denis on November 18, that caused the collapse of an entire floor of an apartment building
The prosecutor did not elaborate on why authorities believed another plot was in the works.
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.
Belgium -- and specifically Molenbeek, a Brussels suburb with a history of links to terrorism
-- has been a focus of the investigation. On Thursday, the nation's threat level was lowered from 4 to 3, the Interior Ministry told CNN.