Russian and French presidents on Thursday agreed to step up cooperation in fight against terrorism, while promising that the incident like the recent downing of Russian fighter jet near the Turkey-Syria border should never happen again, Xinhua news agency reported.

WATCH: Russian warplane shot down in Syria

READ: Putin says still no 'apologies' from Turkey over downed warplane

While describing the talks with visiting French President Francois Hollande as "constructive," Russian President Vladimir Putin said at the joint press briefing that the two sides decided to share military intelligence on combating Islamic State (IS) the terrorist group in Syria, which is a step toward forming an international anti-terror coalition.

The two leaders showed their determination to punish perpetrators of terrorist acts against Russia and France, both of which were victims of terrorist attacks believed to be conducted by the IS.

"We all suffer from terrorism, so we should make concerted efforts. This is the point of our meeting," Hollande said, stressing the urgency to reach consensus on forming a broad global coalition.

Putin and Hollande also believed that forces fighting the IS and other terrorist groups will not be targeted in both countries' military operations in Syria, and vowed to support those forces on the common mission.

Russia launched its air campaign against IS targets in Syria late September at the request of Syrian President Bashar al-Assad, which the Kremlin said have significantly diminished the combat capability of the terrorist group.

France intensified its air strikes against the IS after the militant group conducted a string of deadly attacks in Paris earlier this month, which left at least 129 people dead, with more than 300 others injured.

READ: France launches air strikes against Islamic State in Syria

Difference, however, remains between the two leaders over the future of Assad when it comes to the political solution to the protracted crisis in the war-torn country.

Hollande insisted that Assad could not have any place in Syria's future, while Putin, who viewed Assad and his troops as allies in the fight against terrorism, stressed that the fate of Assad should be decided by the Syrian people.

When asked about the downing of Russian Su-24 warplane by Turkey, Putin warned that Russia would not consider cooperation with any one or any coalition if similar incident happens again.

"We believe that this will not be repeated. Or else any interaction with anyone or any coalition with any party would not be needed by Russia," said Putin.

Hollande said to avoid such incidents from happening again, it is necessary for all countries fighting against terrorists in Syria to strengthen coordination of military forces deployed in the region.

Putin also expressed his disappointment as Turkey only made "vague explanations," without offering full apologies nor collaboration with Russia to prevent similar tragedies from repeating.

"Those claims of Turkey are all excuses, saying they didn't know the Su-24 belongs to Russia," Putin said, noting that the warplane has necessary visual military markings on it.

According to Putin, the Russian-Turkish relation was destroyed "thoughtlessly and stupidly," stressing that "it could not even occur to us that we could receive a blow from a country which we used to consider as an ally."

Putin also doubted the functions of information exchange mechanisms established between Russia and the US-led coalition, as well as inside the coalition itself.

The Russian president insisted all flight information was provided by Russia to the coalition in advance, and "the American side who leads the coalition knew about the place and time of stay of the Russian aircraft during its flight."

Serious consultations would be held with the US on information exchange in Syria in regard to the downing of Su-24, said Putin.

According to him, Russian air forces and Syrian army intensified strikes in the area where the Russian Su-24 fighter jet was downed Tuesday, leaving one of the two pilots killed. The other pilot was later rescued.

Putin stressed that the S-400 air defence system was deployed in Syrian Hmeimim airbase for protection of Russian aircraft located there, "without contradiction of what we do with the coalition."

Putin also urged Ankara to take actions to cut off illegal and"industrial-scale" oil supplies from territories controlled by the IS to Turkey.

In their hours-long talks, Hollande also showed his support for the investigation of the Russian passenger plane crash over Egypt's Sinai Peninsula on Oct 31, which killed all 224 people onboard.

READ: Russian airliner crashes in Egypt's Sinai, all 224 aboard 'killed'

READ: 'Many dead' in Russian plane crash including 17 children - Egypt aviation official

WATCH: Flight recorder reveals noise in plane's final seconds, Egypt says

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The two leaders agreed to continue their dialogue on the sidelines of the upcoming United Nations Climate Change Conference in Paris.