Thomson Reuters
The comments from the president of the European Commission came in the wake of a terrorist attack in Paris on Friday that killed 132 people and left more than 300 others injured.
But the comments are not likely to stave off intense scrutiny of Europe's broadly open-door policies.
One of the attackers reportedly entered Greece with a Syrian passport - the authenticity of which has not been confirmed - on October 3, which has added fuel to calls for Europe to tighten its borders.
"The president of the [French] republic announced a state of emergency and temporary border controls, and that's all well and good,"said Marine Le Pen, the leader of the far-right National Front party who has become known for her strong rhetoric against immigration.
"But what about the European Union? It is essential that France takes back control of its national borders."
Both Juncker and French President Francois Hollande responded to these calls on Sunday by calling for parliementarians to keep discussions on refugees and terrorism separate.
"We should not mix the different categories of people coming to Europe," Juncker said.
Thomson Reuters
"He is a criminal, and not a refugee. And I would like to invite those in Europe who are trying to change the migration agenda we have adopted to be serious about this and not give in to these basic reactions."
Juncker's comments echoed those made by German chancellor Angela Merkel on Saturday in Berlin.
"We believe in the rights of every individual to seek his fortune, in respect for others and in tolerance," Merkel said in her first public statement after the attacks.
"Let us reply to the terrorists by resolutely living our values and by redoubling those values across all of Europe -- now more than ever."
REUTERS/Giorgos Moutafis
"I'd like to appeal urgently that no one rush to make a connection with the refugee situation," German Interior Minister Thomas de Maiziere, a longtime Merkel confidant, told reporters in Berlin. "How we deal with the refugee crisis shouldn't be linked in any way to how we deal with terrorism."
Germany has registered nearly 800,000 asylum-seekers since January 2015.
US President Barack Obama also has no plans to change the US' plans to accept up to 10,000 Syrian refugees, said Ben Rhodes, the deputy national security adviser for strategic communications.
"We're still planning to take in Syrian refugees," Rhodes said on Fox News Sunday, amid backlash from Republican presidential candidates.
But on Sunday, Poland said it will "not respect" the European Council's decision to relocate refugees and immigrants to all EU member countries. The Netherlands has said it will tighten security at its borders and airports. And France and Belgium have temporarily closed their borders.
'Deep ties to France'
But analysts are broadly blaming the attacks on intelligence failures - not refugees.
At least one of the attackers responsible for the massacre in the Bataclan concert hall, which left 89 people dead, was a 29-year-old French national named Ismael Omar Mostefai who had been on the French government's radar since 2010 for his suspected ties to extremists.
Police say it is likely he crossed into Syria between 2013-2014, where he probably received training by militant groups, The Washington Post reported.
A senior European intelligence official familiar with the case named two other attackers as Ibrahim and Salah Abdeslam, two French-born brothers living in Belgium.
Indeed, some experts say it is likely the attackers had closer ties to France than to Syria.
"It would certainly suggest that they'd spent time in Syria," counterterrorism expert Michael Leiter, who served in the administrations of George W. Bush and Barack Obama, told MSNBC's Alex Witt on Saturday.
"But I think we're probably going to find out that these individuals had very, very deep ties to France, which will likely be many of these guys' homeland."
AP/Thibault Camus
The 2004 train bombings in Madrid - which killed 191 people and wounded 1,800 - were carried out by a loose group of Moroccan, Syrian, and Algerian attackers and two Guardia Civil and Spanish police informants.
A series of coordinated suicide attacks in London on July 7, 2005, that killed 52 and injured more than 700 were carried out by four bombers - three of whom were British-born and had been living in Leeds with their families before the attacks. The fourth was Jamaican-born and had been residing in Buckinghamshire with hs pregnant wife and son.
January's attacks on the satirical newspaper Charlie Hebdo and a kosher supermarket in Paris were carried out by two French citizens, Chérif and Saïd Kouachi - born in Paris to Algerian immigrants - and their close friend, Amedy Coulibaly, who was born in a suburb of Paris.
Coulibaly met Cherif in a French prison, where they are believed to have been radicalized by an Al Qaeda recruiter named Djamel Beghal, a French-Algerian.
'Syrians are not terrorists'
Thomson Reuters
"Many news speak about Syrians, police find Syrian passport. Of course I'm worried. It's not good," a 24-year-old tourism student from the northern Syrian town of Hama told AFP on Sunday.
"Syrians are not terrorists. We need life and peace for work."
Ayham al-Khalaf, a Syrian journalist who fled Raqqa in 2014, echoed this sentiment.
"If some French people already mistrusted Arabs, now that hate will increase," al-Khalaf told AFP. "The situation will get harder for us here for sure."
"Following the victims and the terror in Paris, the voices of those who oppose our existence as Syrians in Europe will rise," a Syrian activist living in Germany wrote in Arabic on Facebook on Friday, according to a translation by Vocativ. "They will say that we arrived and brought the terror and the violence and war with us, and they will blame Islam directly as long as it's the religion of most of us."
Thomson Reuters
"I understand some of the European people's concern about the safety and the security of their countries, and it's totally their right to do so, but the refugees are not the cause of the problem and not behind the horrible attacks on Paris," he said. "We are not terrorists or extremists."
One tweet on Friday night, that has since gone viral, summed up why those calling for tighter borders in the wake of the attacks should rethink assigning blame to asylum-seekers.
"To people blaming refugees for attacks in Paris tonight," the tweet read. "Do you not realise these are the people the refugees are trying to run away from..?"