President Obama made remarks and answered questions at the G-20 summit in Turkey on Nov. 13, following the Paris attacks. He spoke out against critics playing "political games" with the U.S. troops in Afghanistan. (AP)

Speaking to reporters in Antalya, Turkey, on Monday, President Obama said his approach to countering the so-called Islamic State "is the strategy that ultimately is going to work" but that the terrorist network still can exact serious damage worldwide.

"But understand that one of the challenges we have in this situation is that if you have a handful of people who don't mind dying, they can kill a lot of people," Obama said in a news conference after the conclusion of the Group of 20 summit there. "That’s one of the challenges of terrorism. It's not their sophistication or the particular weaponry that they possess, but it is the ideology they carry with them and their willingness to die."

[Raids spread across France and Belgium amid manhunt for suspects]

Obama also pointedly addressed the issue of whether the United States and other countries should continue to accept refugees, given the fact that one of the participants in the Paris plot may have come in with Syrian migrants. He said the United States would continue to accept more refugees from Syria and elsewhere, though "only after subjecting them to rigorous screening and security checks."

"Slamming the door in their faces would be a betrayal of our values," he said. "Our nations can welcome refugees who are desperately seeking safety and ensure our own security. We can and must do both."

President Obama decried the calls from some to stop accepting Syrian refugees after the attacks in Paris, saying it would be "a betrayal of our values." (AP)

Without directly naming GOP presidential candidates, the president blasted political leaders for suggesting the United States should accept only Christians fleeing Syria. He alluded to the fact that some of these same politicians -- namely Sen. Ted Cruz (R-Tex.), whose father fled Cuba decades ago - -had benefited from America's willingness to accept refugees.

"And when I hear folks say that, well, maybe we should just admit the Christians but not the Muslims, when I hear political leaders suggesting that there would be a religious test for which person who's fleeing from a war-torn country is admitted, when some of those folks themselves come from families who benefited from protection when they were fleeing political persecution, that's shameful," he said, his voice rising. "That's not American. That’s not who we are. We don’t have religious tests to our compassion."

Presidential candidates Marco Rubio, Jeb Bush, Ben Carson and Bernie Sanders all spoke about strategies to confront terrorism in the wake of the attacks in Paris. (The Washington Post)

[Cruz: ‘No meaningful risk’ of Christians committing terrorism]

The president noted that the world's most prominent Christian leader, Pope Francis, did not frame the Syrian refugee crisis in the same terms as several Republican leaders.

"When Pope Francis came to visit the United States and gave a speech before Congress, he didn't just speak about Christians who were being persecuted, he didn't call on Catholic parishes just to admit those who were of the same religious faith, he said protect people who were vulnerable," Obama said. "And so I think it is very important for us right now, particularly those who are in leadership, particularly those who have a platform and can be heard, not to fall into that trap, not to feed that dark impulse inside of us."

Cruz, for his part, laughed before telling reporters in Sun City, S.C. what he thought about the president's comments.

“It is one of the saddest things we’ve seen for seven years, that President Obama has consistently abandoned and alienated our friends and allies and has coddled and appeased our enemies. And that is never more true than with radical Islamic terrorism," he said. "Both President Obama and Hillary Clinton want to define the enemy as some sort of abstract and ill-defined violent extremism. That means they cannot direct a strategy to defeat it because they cannot acknowledge who they’re fighting."

At other points in the news conference Obama repeatedly defended his military, counterterrorism and diplomatic strategy against Islamist extremists, saying that it represents the only sustained way degrade the Islamic State, also known as ISIS and ISIL, and to resolve Syria's protracted civil war.

"So, there will be an intensification of the strategy we put forward, but the strategy that we are putting forward is the strategy that ultimately is going to work," Obama said, adding that he encouraged the other leaders at the summit to contribute more in terms of military and humanitarian resources.

He also reiterated that he was unwilling to dispatch major ground troops to Syria in order to confront the threat there.

"The one exception is that there had been a few who suggested that we should put large numbers of U.S. troops on the ground," he said, "And it is not just my view, but the view of my closest military and civilian advisers that that would be a mistake, not because our military could not march into Mosul or Raqqa or Ramadi and temporarily clear out ISIL, but because we would see a repetition of what we've seen before, which is if you do not have local populations that are committed to inclusive governance and who are pushing back against ideological extremes, that they resurface unless we're prepared to have a permanent occupation of these countries."

The president had sharp words for some of his critics, arguing that they have not offered a detailed strategy that is different from his, beyond calling for additional ground troops.

"I think that, when you listen to what they actually have to say, what they're proposing, most of the time, when pressed, they describe things we're already doing," Obama said. "Some of them seem to think that, if I was just more bellicose in expressing what we're doing, that that would make a difference. Because that seems to be the only thing that they're doing, is talking as if they're tough."

"My only interest is to end suffering and to keep the American people safe," he added, saying that he was open to other ideas. "But we do not do, what I do not do, is to take actions either because it is going to work politically or it is somehow, in the abstract, make America look tough or make me look tough."

Noting that he regularly visits wounded soldiers at Walter Reed Medical Center, the president said he was well aware of the cost of war.

"And I see a 25-year-old kid that is paralyzed or has lost his limbs. And some of those are people I've ordered into battle," he said. "So I can’t afford to play some of the political games that others may."

Under repeated questioning by reporters, the president appeared annoyed at times. Asked again by CNN's Jim Acosta why the United States would not take more aggressive action, Obama replied, "Well, Jim, I just spent the last three questions answering that very question. So, I don’t know what more you want me to add."

Asked whether the United States had advance warning of the Paris attacks, Obama said that while American intelligence regularly detects hints of possible threats, "there were no specific mentions of this particular attack that would give us a sense of something that we need -- that we could provide French authorities, for example, or act on ourselves."

Katie Zezima contributed to this report.