"There is a lot on the table for the North Koreans if they choose to take it," Rice said in a Monday interview with the Times editorial board while attending talks on the sidelines of a United Nations summit.
The State Department provided a transcript of the interview to other news outlets late Monday.
Normalization of US-North Korea ties could be expected if Pyongyang made a "strategic choice" to disband its nuclear weapons arsenal, according to Rice.
"I think that they can expect to have, if they are prepared to make the strategic choice to give up their nuclear weapon, give up their nuclear programs, they expect to have a road toward normalization of relations with the United States and possibly with Japan if they can fix the abduction problem," Rice said.
Japan has pressed North Korea to come clean on its kidnappings of Japanese nationals in the 1970s and 1980s.
Rice's statement came ahead of the resumption Tuesday of six-party talks among the United States, the two Koreas, China, Japan and Russia aimed at ending North Korea's nuclear weapons drive.
The talks have been going on for more than two years without any breakthrough.
The United States has no diplomatic relations with North Korea. Pyongyang had demanded normalization of ties, among other conditions, for progress to be made at the nuclear disarmament talks.
In what was seen as a policy shift, Washington called North Korea a sovereign nation in July as part of an effort to woo the hardline communist state to the negotiating table.
"If the North Koreans really do want an entry into the international system, it's there if they're prepared to verifiably dismantle their nuclear weapon programs," Rice said.
"So we'll see whether or not they've made that strategic choice," she said.
Rice also said the United States was more respectful of North Korea following its return to the negotiating table in July after boycotting it for more than a year.
"But now that they're there, you know, we'll be respectful. We're in negotiation with them," she said.
However the chief US diplomat said the United States would not stop raising the issue of human rights in North Korea, warning that Pyongyang would face problems if it deprived its people of their basic rights.
Non-governmental groups have accused North Korean dictator Kim Jong Il's regime of widespread human rights abuses, including deliberate starvation, abduction, family separations, religious persecution, trafficking of women and children, inhumane prison conditions, the use of gas chambers and the likely practice of genocide.
"When I said that they were sovereign, that seemed to make a big deal but it seemed to me a statement of fact. I think they are sovereign. So I think we can manage this but we're not going to stop talking about human rights," Rice said in the interview.
"It's important to us. And it's important that light be shone on that and ultimately it backfires if you are not prepared to try to make a society more open; it backfires even on your ability to try and verify arms control agreements, for instance."