Updated: 12:10 p.m. ET
(CBS News) Amid ongoing controversy surrounding a recent spate of national security leaks, President Obama on Friday disputed the notion that the leaks had come from the White House and pledged that "if we can root out folks who have leaked, they will suffer consequences."
"In some cases, it's criminal -- these are criminal acts when they release information like this. And we will conduct thorough investigations, as we have in the past," Mr. Obama said, speaking to reporters in the White House press briefing room. "We will conduct thorough investigations as we have in the past."
After the recent publication of several New York Times articles containing what would appear to be high-level security information -- including pieces about Mr. Obama's alleged "kill list," U.S. cyber attacks on Iran and more -- concerns have been raised about the source of the leaks, which have been condemned by Democrats and Republicans alike.
Republican Senator John McCain, Mr. Obama's Republican presidential rival in 2008, hasfor political gain.
"This is a breach of national security. And ... you can put lipstick on a pig but it's still a pig," McCain said on "CBS This Morning" this week. McCain has since announced that he is planning to introduce a Senate resolution calling for a special investigation of the leaks.
Mr. Obama disputed the contention that the leaks had come from the White House, a charge he characterized as "offensive" and "wrong."
"The notion that the White House would purposely release classified national security information is offensive, it's wrong, and you know, people I think need to have a better sense of how I approach this office and how people around me here approach this office," he said.
"It is a source of consistent frustration, not just for my administration, but for previous administrations when this stuff happens," the president said. "And we will continue to let everybody know in government -- or after they leave government -- that they have certain obligations that they should carry out."
Mr. Obama also noted that "the writers of these articles have all stated unequivocally that [the leaks] didn't come from this White House."
"That's not how we operate," he said.
David Sanger, who wrote the Times story suggesting Mr. Obama had secretly ordered sophisticated cyberattacks on the computers that run Iran's main nuclear enrichment facilities, suggested in a recent appearance on "Face the Nation" that the White House had not fed him the story.
"I spent a year working the story from the bottom up, and then went to the administration and told them what I had," he told Bob Schieffer. "Then they had to make some decisions about how much they wanted to talk about it. All that you read about this being deliberate leaks out of the White House wasn't my experience."
Democratic Senator Dianne Feinstein, who chairs the Senate Intelligence Committee, told reporters Thursday the committee members were "extremely upset" about the "cascade of leaks coming out of the intelligence community over the last several weeks and months."
"It's our clear intention to put a stop to this in the best way that we can," she said.
When asked about the possibility of bringing in a special prosecutor to investigate the leaks, however, Feinstein said she needed a "little more time to look at" the option.
"A special prosecutor can take years," she said. "We don't have years. We need to legislate, we need to get some solutions before us very quickly."