U.S. President Barack Obama and French President Francois Hollande vowed on Tuesday to intensify their attacks against the Islamic State group, coming 11 days after jihadists killed 130 people in the French capital of Paris. The two set clear limits on the future level of military engagement, and Obama stopped short of endorsing a French proposal for a unified coalition that would include Russia, according to USA Today.

"We are here to declare that the United States and France stand united in total solidarity to deliver justice to terrorists and those who sent them, and to defend our nations," Obama told Hollande, switching into his language to tell him, "We are all French," according to AFP.

"As Americans, we stand by our friends in good times and in bad," Obama told reporters after meeting with Hollande for two hours in the Oval Office for the first time since the Nov. 13 terrorist attacks.

Obama said the two countries will "deliver justice" to the perpetrators of the attacks and to "those who sent them." The "murderous ideology" of the Islamic State group poses a serious threat and "cannot be tolerated. It must be destroyed. And we must do it together," Obama said, according to USA Today.

No new major shifts in strategy were announced, but Obama said the U.S. would "step up" its coordination with France by providing it with additional intelligence and air support. He also asked the European Union to implement an agreement that would require airlines to share passenger data.

Hollande said France will increase its airstrikes against the Islamic State group in Syria and Iraq, but like Obama, explicitly ruled out ground troops. "France will not intervene militarily on the ground," Hollande said. "It is for the local forces to do so."

The meeting came the same day Turkey shot down a Russian warplane that was allegedly violating its airspace, an accusation Russia denies. Also on Tuesday, U.S.-backed Syrian rebels armed with U.S.-supplied anti-tank missiles reportedly shot down a Russian rescue helicopter searching for the pilot of the warplane.

Hollande and Obama warned Russia against any escalation over the incident with Turkey and said it is still important that the two countries are talking to each other, according to CBS News.

"I think it is very important for us to right now make sure that both the Russians and the Turks are talking to each other and find out exactly what happened, and take measures to discourage any kind of escalation," Obama told reporters, adding that Turkey had a right to defend its airspace.

Obama also complained about the "ongoing problem with the Russian operations in the sense that...they are going after moderate opposition" that are armed and trained by the U.S. and fighting to overthrow Syrian President Bashar al-Assad.

But Obama appealed to the Russians as well, saying they could have a more constructive role in the coalition is they stop propping up Assad.

"Given Russia's military capabilities and the influence they have on the Assad regime, them cooperating would be enormously helpful in bringing about resolution of the civil war in Syria," Obama said, according to AFP.

"If and when they do, it will make it easier for us to go after ISIL," he added.

Hollande is set to meet with Russian President Vladimir Putin on Thursday to discuss increasing their cooperation with a unified coalition, but the incident with Turkey complicates that prospect.