The two met Wednesday at police headquarters in lower Manhattan, CBS2's Janelle Burrell reported.
"Please don't let those savages accomplish what they want to accomplish," Comey said of terrorists.
Comey and Bratton urged the public not to live in fear in the wake of threats by the Islamic State group but wanted Americans to know they are the eyes and ears of law enforcement if they see something suspicious.
"Because it is increasingly a challenge for us to see the threat," Comey said. "Somebody radicalizing ... may only show signs of radicalization to a very small group of people."
He said, unlike al Qaeda, the Islamic State group is focused on smaller attacks, sending the message to come fight with them in the Middle East or kill where you are, WCBS 880's Rich Lamb reported.
Comey said a lot of terrorists and their sympathizers are now communicating through encrypted messaging systems that they cannot access.
Comey pointed to the mass shooting in San Bernardino, California. He said the FBI is still trying to trace the final hours of the two suspected killers, who he says were not part of an organized terror cell.
"So where were they four hours after the attack?" Comey said. "And what else, if anything, were they planning to do? And was there anybody who helped them or assisted them or supported them in some way?"
The FBI director said, contrary to what several people have claimed, neither of the attackers committed to jihad on social media, 1010 WINS' Steve Kastenbaum reported. He said those kind of statements were only made in private direct messages between the two.
Bratton and Comey touted the 35th anniversary of the Joint Terrorism Task Force, the partnership between the NYPD and FBI, a union they say will have an even wider reach as the Isalmic State group seeks to recruit more to its cause.
"We are significantly ramping up in New York City capabilities to address the new threat, the threat of ISIS effectively going in so many new directions and utilizing social media to facilitate going those directions," Bratton said.
"We are not perfect," Comey said. "In my view, we are never good enough."
The FBI director was asked about the threats made against schools in New York City and Los Angeles on Tuesday and the vastly different responses to the email threats. He refused to give his opinion, saying he was not part of that communication process.
Meanwhile in Washington, Homeland Security Secretary Jeh Johnson announced, among other changes, an increased focus on airports.
"Earlier this year, TSA and I issued guidance with regard to airport security," he said. "More guidance on airport security is forthcoming."
Johnson also announced modifications to the National Terrorism Advisory System.
The new system includes three classifications:
* A bulletin, which describes developments of general trends regarding threats of terrorism
* An elevated alert, which warns of a credible terrorism threat against the United States
* An imminent alerts, which warns of a credible, specific and impending terrorism threat against the U.S.
In conjunction with the announcement, Homeland Security issued its first "bulletin" under the new system, which remains in effect through June 16.
"We want to put in one place for the public to see what we are seeing concerning the homeland and what we are doing about it and what the public can do about it," Johnson said.
The Department of Homeland Security released its first bulletin today, CBS2's Alice Gainer reported.
"We are in a new phase in the global threat environment, which has implications on the homeland," the bulletin says. "Particularly with the rise in use by terrorist groups of the Internet to inspire and recruit, we are concerned about the "self-radicalized" actor(s) who could strike with little or no notice. Recent attacks and attempted attacks internationally and in the homeland warrant increased security, as well as increased public vigilance and awareness."
The previous alert system, which was created in 2011, had never been triggered because a credible terrorist threat was necessary to warrant an alert. That replaced a system of colors put in place after 9/11.
Johnson said recently that officials needed to take the mystery out of the global terror threat and better explain what they're doing and what the public should do, WCBS 880's Paul Murnane reported.
Administration is improving security and screening at airports and the K-1 Fiancee Visa Program is under review. The fiancee visa program is how Tashfeen Malik, the female San Bernardino shooter, was able to get into the United States.
The bulletins and other information can be accessed on the Homeland Security website, or on social media. They will also be announced publicly.
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