By mentioning the security of the “U.S. mainland,” North Korea has appeared to challenge Washington to appease the North with dialogue and concessions or face the prospect that North Korea will continue to expand its nuclear weapons and long-range missile programs.

Washington has said that North Korea is trying to build intercontinental ballistic missiles that are capable of reaching the United States, and nuclear warheads that are small enough to mount on them, although American intelligence agencies differ over how close the North is to mastering such technologies. North Korea successfully launched a satellite into orbit on a three-stage rocket in December and conducted its third nuclear test in February in what it called an attempt to “miniaturize” a warhead.

Kim Yong-hyun, a professor of North Korean studies at Dongguk University in Seoul, said he did not “see any fundamental change in the North Korean position” in the latest statement.

The North’s statement also said that the denuclearization of the peninsula must include “totally ending the U.S. nuclear threats,” essentially repeating the North’s long-held position that it would discuss dismantling its nuclear weapons programs but only as part of broader nuclear arms reduction talks in the region.

The latest North Korean overture comes after the summit meeting between President Obama and the Chinese president, Xi Jinping, this month. Mr. Xi is scheduled to meet with President Park Geun-hye of South Korea by month’s end.

Both Washington and Seoul have been trying to enlist the help of China, the North’s traditional ally, to check the North’s nuclear ambitions. Some analysts view North Korea’s recent proposals of dialogue as attempts to create a rift between Beijing, which favors a negotiated end to the North’s nuclear crisis, and Washington and Seoul, which insist that diplomacy as well as economic sanctions are necessary to change the North’s course.