Washington (CNN) Turkey's downing of a Russian fighter plane shouldn't lead to further wartime escalation in the region, President Barack Obama insisted at a press conference Tuesday.

But he maintained that Turkey had a right to defend its airspace and charged that Russian air activity near the Turkey-Syria border has contributed to the crisis.

"This points to an ongoing problem with the Russian operations," Obama said. "They are operating very close to a Turkish border, and they are going after moderate opposition that are supported by not only Turkey but a wide range of countries."

Turkey said Tuesday it shot down the Russian plane with a missile strike after repeated warnings to the plane that it had flown over its territory.

Photos: Turkey-Syria border: Russian warplane crashes Photos: Turkey-Syria border: Russian warplane crashes A Russian warplane goes down in Syria's Bayirbucak region, near the Turkish border, on November 24, 2015. Hide Caption 1 of 6 Photos: Turkey-Syria border: Russian warplane crashes The Turkish military says it shot down the unidentified warplane, contending it repeatedly violated Turkish airspace. Hide Caption 2 of 6 Photos: Turkey-Syria border: Russian warplane crashes Turkey's semi-official Anadolu Agency cites Turkish presidential sources in reporting that a Russian SU-24 was "hit within the framework of engagement rules." Hide Caption 3 of 6 Photos: Turkey-Syria border: Russian warplane crashes The Anadolu Agency reported that a parachute was also seen leaving the jet before it crashed. The fate of the airman remains unclear. Hide Caption 4 of 6 Photos: Turkey-Syria border: Russian warplane crashes The Turkish government is strongly opposed to the Syrian regime of Bashar al-Assad. Russia, however, has backed Assad, and has had warplanes active over Syria. Hide Caption 5 of 6 Photos: Turkey-Syria border: Russian warplane crashes Heavy smoke has been seen in the area where the plane fell.

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Obama urged Russia and Turkey to communicate about the details of the operation in order to decrease the chance of escalation, a message the White House said Obama relayed in a later phone conversation with Turkish President Recep Tayyip Erdogan.

The downing of the Russian plane complicated Hollande's visit to the White House, where he pressed Obama for greater global cooperation on battling ISIS , including with Moscow. Obama appeared resistant to forming any new alliances in battling ISIS, saying he'd already convened more than 60 nations in a bid to curb the group's territorial gains in Iraq and Syria.

Hollande has openly called for a greater international effort to push back ISIS , whose killing spree in Paris two weeks ago was the worst terror attack on French soil in more than half a century.

He said Tuesday greater cooperation between the United States and Russia is required in battling ISIS, though persistent U.S. skepticism about Putin's intentions in Syria have until now prevented any significant military coordination between the two countries.

Photos: Political violence is driving terrorism Photos: Political violence is driving terrorism A Nigerian policeman inspects the site of a suicide attack by Boko Haram at a busy cattle market in the northeastern Nigerian city of Maiduguri in June, 2015. Boko Haram overtook ISIS as the world's deadliest terror group last year, according to the Global Terrorism Index, while Nigeria had the biggest year-on-year increase in terrorism, with deaths up more than 300%. Hide Caption 1 of 6 Photos: Political violence is driving terrorism In this image taken from social media, an ISIS fighter holds the group's flag as he stands on a tank, purportedly captured when they took over the town of Qaryatain, Syria. ISIS, along with Boko Haram, is one of two groups accounting for 51% of claimed terrorism deaths in 2014. Hide Caption 2 of 6 Photos: Political violence is driving terrorism A member of the Iraqi security forces fires ammunition in Baghdad in 2014 during a funeral procession of an Iraqi politician. The deadliest city in the world for terrorism is Baghdad. There were 2,454 deaths in Baghdad in 2014, with a death rate from terrorism of 43 per 100,000 people. Hide Caption 3 of 6 Photos: Political violence is driving terrorism Iraqi counter-terrorism forces patrol a street in Tikrit in April 2015, a day after the country's prime minister declared victory in the battle to retake the city from ISIS. Hide Caption 4 of 6 Photos: Political violence is driving terrorism An Iraqi Kurdish Peshmerga fighter prepares an ammunition belt as he guards a position at the frontline of fighting against ISIS militants near the northern Iraqi town of Sinjar. Hide Caption 5 of 6 Photos: Political violence is driving terrorism A Syrian family waits after arriving on the Greek island of Lesbos along with other migrants and refugees, on November 17, 2015. Ten of the 11 countries most affected by terrorism also have the highest rates of refugees. Hide Caption 6 of 6

"We want to gather all countries," Hollande said. "We do not want to exclude anyone."

But he also said Russia must pledge to target ISIS terrorists instead of moderate Syrian forces opposed to the government of Bashar al-Assad , a requirement Obama also insisted upon during Tuesday's press conference.

"Russia right now is a coalition of two -- Iran and Russia -- supporting Assad," Obama said.

"Russia's the outlier," he added, noting that strikes against moderate opposition fighters "bolster the Assad regime."

Obama also cited the incident with Turkey as a reason for Russia to turn its focus to fighting only ISIS in Syria, saying that "some of those conflicts or potential for escalation are less likely to occur" if it narrowed its sights.

He said the encounter "underscores the importance of our moving the political track along as quickly as possible" when it comes to resolving the Syrian civil war, which ISIS has exploited to seize territory.

After the press conference, Vice President Joe Biden told reporters gathered in the East Room that he believed "Putin is coming to the realization that Assad should transition out."

called on Europe to do more to stop the flow of foreign fighters, share passenger lists and exchange information across borders. Without any major new commitments to announce alongside Hollande, Obama instead touted a new intelligence sharing agreement announced last week that has helped France target ISIS sites in Raqqa, Syria . And hecalled on Europe to do more to stop the flow of foreign fighters, share passenger lists and exchange information across borders.

Calling ISIS a "scourge" that "must be defeated," Obama said the U.S. stood with France after the brutal massacre in Paris.

"We'll deliver justice to these terrorists and those who sent them," Obama said. ISIS "cannot be tolerated. It must be destroyed. And we must do it together."

Later on Tuesday Obama convened his National Security Council to discuss counter-ISIS strategy. That amid a State Department-issued warning to travelers about potential terror threats. The White House said in a statement Tuesday night "the President was briefed that there is currently no specific, credible threat to the homeland from ISIL."

Hollande's visit to Washington comes amid a spate of jet-set diplomacy for the French leader. He'll meet with Russian President Vladimir Putin on Thursday, and German Chancellor Angela Merkel Wednesday. He met in Paris with British Prime Minister David Cameron Monday.

Obama, who returned from a week-long foreign swing on Monday, made clear in the aftermath of the Paris attacks he wasn't considering a change in strategy , saying instead he was planning to intensify the U.S.-led coalition's air campaign in Iraq and Syria.

In his first press conference after the attacks, in Antalya, Turkey, Obama argued testily that alternative plans from Republicans ignored realities on the ground, saying that his own interactions with wounded troops instilled a wariness toward war.

After coming under intense criticism for his response to the attacks, Obama turned up his rhetoric on ISIS Sunday , saying during a press conference in Malaysia that his efforts to stamp out the group would succeed.

But he nonetheless departed Asia insisting the strategy he's utilized against ISIS is working -- and that other options, like sending in ground troops, aren't being considered.

The White House signaled Monday that it already believes U.S. contributions to the anti-ISIS effort are sufficient.

"The United States is certainly pulling more than our own weight when it comes to the contribution behind this coalition," White House Press Secretary Josh Earnest said. "That's something that we're glad to do. That is in line with the long tradition of American leadership. It certainly is a tradition that this president believes in."