The president insists he hasn't given up on gun control, but he said he's had difficulties getting changes passed through Congress in the years since the Sandy Hook Elementary School shooting.

"What we've done is to try to do as much as we could administratively to tighten up how background checks are run, to go after illegal drug runners," President Obama told ABC News's Dr. Richard Besser during a sit-down interview at Howard University. "But I will tell you that trying to get something through Congress has proven to be very difficult. And it's heart-breaking."

Besser reminded Obama that he promised to be tougher on gun control after the Sandy Hook Elementary School shooting, in which a gun-wielding intruder shot 20 children and six adults in December 2012.

After the incident, the president promised stronger gun control. But Besser pointed out that it has been more than a year since his administration has taken any action on this subject.

"You know, those two or three days after the Sandy Hook shooting are some of the worst days of my presidency because I met those families right after," Obama said. "And you're talking about 6-year-olds who were just systematically murdered. And that may be one of the few times where I was just shocked that Congress didn't act."

Obama said his administration is continuing to take steps toward tighter gun policies. He said most gun owners recognized the need for "common sense gun safety laws."

"But the power of NRA and the gun lobby in Congress is formidable," Obama said. "And you know, we're going to keep chipping away at this, but until you get intense public demands for this, it's probably not going to happen because some special interests and lobbyists in Washington are really, really strong and their membership feels very intensely about the issue. Whereas the general public is concerned about it, but doesn't make it their top priority."

You can see the whole interview on "Good Morning America."

ABC News's Lana Zak and Dan Childs contributed to this report.