President Barack Obama took ultimate responsibility on Tuesday for issues around last month's terrorist attack on the U.S. consulate in Benghazi, Libya.

"I am ultimately responsible for what's taking place there because these are my folks, and I'm the one who has to greet those coffins when they come home," Obama said during a debate with Republican presidential challenger Mitt Romney in New York.

"These are just representatives of the United States, they are my representatives. I send them there, often times into harms way," Obama said.

Obama's remarks came a day after Secretary of State Hillary Clinton told CNN's Elise Labott that she took responsibility for the security in Benghazi. That's where the U.S. mission was overrun on September 11, killing Ambassador Christopher Stevens and three other Americans.

"Secretary Clinton has done an extraordinary job," Obama said in response to a follow-up question from CNN's Candy Crowley who served as the debate moderator. "But she works for me. I'm the president and I am always responsible."

After learning about the attack, Obama told the debate audience at Hofstra University that he called his national security team with instructions for how he wanted the situation handled.

In addition to ordering an increase in security at all U.S. diplomatic missions in Libya and across the region, Obama said he ordered an investigation to find out exactly what happened "regardless of where the facts lead us to make sure folks are held accountable and it doesn't happen again."

The president said he also told his team the United States was "going to find out who did this and hunt them down."

Obama also accused GOP nominee Mitt Romney of playing politics on national security by releasing a statement critical of the administration with the attack still in progress.

Romney questioned at the debate how long it took Obama to refer to the incident in Benghazi as a terrorist attack.

Obama said he called it an act of terror in Rose Garden comments the next day, but Romney challenged him on that point.

"I want to make sure we get that for the record because it took the president 14 days before he called the attack in Benghazi an act of terror," Romney said.

"Get the transcript," Obama replied testily.

While Obama did refer to the incident as an act of "terror" in the Rose Garden, Romney's assertion was not entirely inaccurate.

In a televised town hall forum on Univision on September 20, Obama said the Benghazi incident arose from protests "because of the outrage" over an anti-Muslim video was "used as an excuse by extremists to see if they can also directly harm U.S. interests."

In a subsequent interview with ABC's 'The View' on September 25, Obama said while "extremist militias" were expected to have been involved, he declined to label the assault on the consulate in Benghazi as a terrorist attack, and cited an ongoing investigation to assure the attack "wasn't just a mob operation."

Those comments were days after National Counter-terrorism Center Director Matthew Olsen went on record, on September 19, in testimony before the U.S. Senate, and referred to the attack in Benghazi as a terrorist attack.