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

“If you have a handful of people who don’t mind dying, they can kill a lot of people,” Obama said, in a press conference after the conclusion of the G-20 summit there. “That’s one of the challenges of terrorism.”

Obama also pointedly addressed the issue of whether the U.S. 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 that while any refugees to the U.S. would undergo “rigorous” screening, his government would continue to accept them.

“Slamming the door in their faces would be a betrayal of our values,” he said.

Without directly naming GOP presidential candidates, the president blasted political leaders for suggesting the U.S. should only accept Christians fleeing Syria.

“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.”

Obama repeatedly defended his military, counter-terrorism and diplomatic strategy against Islamist extremists, saying that it represents the only sustained way degrade the Islamic State, also known as ISIL, and to resolve Syria’s protracted civil war.

“There will be an intensification of the strategy that we have 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.

“There have been a few that have suggested that we should put large numbers of U.S. troops on the ground,” he said, noting that past conflicts in Iraq and Afghanistan have shown, “If you do not have local populations that are committed to inclusive governments and are pushing back against ideological extremes, then they resurface.”

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

“When you listen to what they actually have to say, what they’re proposing, most of the time, when pressed, they describe things that we are already doing,” Obama said, adding his political opponents seem to imply if he was “more bellicose in expressing what we’re doing, that would make a difference. Because that seems to be the only thing they’re doing, 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 the one thing he will rule out is adopting a tactic “because it is going to work politically, or it is going to somehow in the abstract going to make America look tough, or make me look tough.”

Noting that he regularly visits wounded soldiers at Walter Reed Medical Center, some of whom have suffered their injuries after being ordered into battle under his watch, Obama said he has seen first-hand the cost of sending Americans to war. “So I can’t afford to play some of the political games that others do.”

Under repeated questioning by reporters, the president appeared annoyed at times. Asked again by CNN’s Jim Acosta why the U.S. would not take more aggressive action, Obama noted that the three previous questions had addressed that issue. “I don’t’ know what more you want me to add.”

Asked whether the U.S. 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” law enforcement or the military the chance to disrupt the plot.