The former first lady also acknowledged that the State Department changed its approach in trying to free the two journalists captured, imprisoned and sentenced to years of hard labor by North Korea. In June, Clinton told ABC News' George Stephanopoulos that the charges against Euna Lee and Laura Ling were "absolutely without merit or foundation."
But, earlier this month, her words sounded more like an apology.
"The two journalists and their families have expressed great remorse for this incident and I think everyone is very sorry it happened," Clinton said at a State Department town hall meeting.
Clinton has said the United States is not apologizing but then added in the ABC interview that "we're sorry."
"The young women themselves have, apparently, admitted that they probably did trespass so they are deeply regretful and we are very sorry it's happened," Clinton said. "Our most important goal is to make sure they get home safe."
Clinton said the North Korean government had not asked her to apologize, but they are "always making demands."
Asked if she was hopeful they would be released, she said, "I'm very hopeful. It's something that I feel very strongly about personally as well as in my capacity as secretary of state. I've met with the families, the anguish they're going through, and their feelings are so painful and I want these young women home."
Iran is also high on the secretary of state's agenda. It remains unclear if the country, where a disputed election that put President Ahmadinejad back into power created a series of violent clashes, will make an overture toward the Obama administration. Clinton said the time for engagement is running out.
"There's a series of choices that clearly Iran needs to make and we're waiting to see if, maybe, they will," Clinton said.
On Obama's offer to meet with Iranian leadership and and how long it is on the table, Clinton said the United States is "willing to have a bilateral discussion with Iran, we also know the nuclear clock is ticking. ... The president has talked about the fall -- the end of the year -- it's just clear that we are not leaving it open for ever, it's not indefinite."
Clinton also addressed Israel and Prime Minister Benjamin Netanyahu's remarks that Jews have the right to settle in east Jerusalem. Obama has repeatedly called for Israel to curb its settlements and establish dialogue with Palestinians.
"I think that we are seeing the government of Israel stake out public positions that necessarily have nothing to do with the settlements," she said.
North Korea and Iran may be the hot-button issues right now, but the secretary of state is facing challenges from other fronts as well. India gave her the cold shoulder on climate change emissions caps, with Environmental Minister Jairam Ramesh saying that "India's position, let me be clear, is that we are simply not in the position to take legally binding emissions targets."
The United States wants the world's largest developing economies to cut emissions to curb climate change, but India and others argue it would stunt their economic growth. Clinton denied that she was rebuffed by the Indians on United States' global climate policy.
"I actually found it to be a very mature and honest exchange of ideas," she told ABC News.
Clinton invited India's prime minister Manmohan Singh on Obama's behalf to Washington in November for a state visit, the first for India in the new administration. The climate change talks are likely to continue then.